{"id":4500,"date":"2016-05-16T11:49:00","date_gmt":"2016-05-16T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/"},"modified":"2018-05-04T15:01:00","modified_gmt":"2018-05-04T09:31:00","slug":"ncert-solutions-class-12-maths-exercise-8-2","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 8.2"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#NCERT_Solutions_class_12_Maths_Applications_of_Integrals\" >NCERT Solutions class 12 Maths\u00a0Applications of Integrals<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#NCERT_Solutions_class_12_Maths_Exercise_82\" >NCERT Solutions class 12 Maths Exercise 8.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#2_Find_the_area_bounded_by_the_curves_and\" >2. Find the area bounded by the curves \u00a0and \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#NCERT_Solutions_class_12_Maths_Exercise_82-2\" >NCERT Solutions class 12 Maths Exercise 8.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#3_Find_the_area_of_the_region_bounded_by_the_curves_and\" >3. Find the area of the region bounded by the curves \u00a0and \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#NCERT_Solutions_class_12_Maths_Exercise_82-3\" >NCERT Solutions class 12 Maths Exercise 8.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#4_Using_integration_find_the_area_of_the_region_bounded_by_the_triangle_whose_vertices_are_1_3_and_3_2\" >4. Using integration, find the area of the region bounded by the triangle whose vertices are \u00a0(1, 3) and (3, 2).<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#NCERT_Solutions_class_12_Maths_Exercise_82-4\" >NCERT Solutions class 12 Maths Exercise 8.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#5_Using_integration_find_the_area_of_the_triangular_region_whose_sides_have_the_equations_and\" >5. Using integration, find the area of the triangular region whose sides have the equations \u00a0and \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#NCERT_Solutions_class_12_Maths_Exercise_82-5\" >NCERT Solutions class 12 Maths Exercise 8.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#6_Choose_the_correct_answer\" >6. Choose the correct answer:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#NCERT_Solutions_class_12_Maths_Exercise_82-6\" >NCERT Solutions class 12 Maths Exercise 8.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#7_Choose_the_correct_answer\" >7. Choose the correct answer:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#NCERT_Solutions_class_12_Maths_Exercise_82-7\" >NCERT Solutions class 12 Maths Exercise 8.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/#CBSE_App_for_Class_12\" >CBSE App for Class 12<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Exercise 8.2 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p><strong>Download\u00a0<a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics-application-of-integrals\/1292\/ncert-solutions\/5\/\">NCERT solutions for Applications of Integrals \u00a0<\/a>as PDF.<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/12%20Maths%20Book%20Part-02%20.jpg\" alt=\"NCERT Solutions class 12 Maths Exercise 8.2\" width=\"176\" height=\"226\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Applications_of_Integrals\"><\/span>NCERT Solutions class 12 Maths\u00a0Applications of Integrals<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>1. Find the area of the circle <\/strong><img decoding=\"async\" style=\"height: 24px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image001.png\" \/><strong>\u00a0which is interior to the parabola <\/strong><img decoding=\"async\" style=\"height: 24px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image002.png\" \/><strong>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><strong>Step I<\/strong>. Equation of the circle is <img decoding=\"async\" style=\"height: 24px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image001.png\" \/><\/p>\n<p><img decoding=\"async\" id=\"Picture 29\" style=\"height: 170px; width: 192px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image003.jpg\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image005.png\" \/>\u00a0 \u2026\u2026\u2026.(i)<\/p>\n<p>Here centre is (0, 0) and radius is <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image006.png\" \/><\/p>\n<p>Equation of parabola is <img decoding=\"async\" style=\"height: 24px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image007.png\" \/>\u00a0\u2026..(ii)<\/p>\n<p><strong>Step II.<\/strong> To find values of <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image008.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image009.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 24px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image007.png\" \/>\u00a0in eq. (i), <img decoding=\"async\" style=\"height: 41px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image010.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 24px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image011.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 24px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image012.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 24px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image013.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image014.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image015.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image016.png\" \/>\u00a0or <img decoding=\"async\" style=\"height: 21px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image017.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image018.png\" \/>\u00a0or <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image019.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image018.png\" \/>\u00a0in <img decoding=\"async\" style=\"height: 24px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image007.png\" \/>,<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 45px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image020.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image019.png\" \/>\u00a0in <img decoding=\"async\" style=\"height: 24px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image007.png\" \/>,<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 45px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image021.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image022.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Points of intersections of circle (i) and parabola (ii) are A<img decoding=\"async\" style=\"height: 45px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image024.png\" \/>\u00a0and B<img decoding=\"async\" style=\"height: 45px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image025.png\" \/><\/p>\n<p><strong>Step III<\/strong>. Area OBM = Area between parabola (ii) and <img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image026.png\" \/>axis<\/p>\n<p>= <img decoding=\"async\" style=\"height: 75px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image027.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 45px; width: 203px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image028.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 75px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image029.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 51px; width: 199px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image030.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 99px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image031.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 67px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image032.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 47px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image033.png\" \/>\u00a0\u00a0\u2026\u2026\u2026.(iii)<\/p>\n<p><strong>Step IV<\/strong>. Now area BDM = Area between circle (i) and <img decoding=\"async\" style=\"height: 17px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image026.png\" \/>axis<\/p>\n<p>= <img decoding=\"async\" style=\"height: 75px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image034.png\" \/>\u00a0\u00a0\u00a0<img decoding=\"async\" style=\"height: 45px; width: 207px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image035.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 75px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image036.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 61px; width: 248px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image037.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 113px; width: 212px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image038.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 83px; width: 340px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image039.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 53px; width: 247px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image040.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 155px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image041.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image042.png\" \/>\u00a0\u2026\u2026.(iv)<\/p>\n<p><strong>Step V<\/strong>. Required shaded area = Area AOBDA<\/p>\n<p>= 2 (Area OBD) = 2 (Area OBM + Area MBD)<\/p>\n<p>= <img decoding=\"async\" style=\"height: 56px; width: 207px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image043.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 48px; width: 204px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image044.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 184px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image045.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image046.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 48px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image047.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image048.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 48px; width: 153px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image049.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_82\"><\/span>NCERT Solutions class 12 Maths Exercise 8.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"2_Find_the_area_bounded_by_the_curves_and\"><\/span><strong>2. Find the<\/strong><strong> area bounded by the curves <img decoding=\"async\" style=\"height: 29px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image050.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image051.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong>Equations of two circles are<\/p>\n<p><img decoding=\"async\" id=\"Picture 32\" style=\"height: 158px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image052.jpg\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 24px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image053.png\" \/>\u00a0\u00a0 \u2026\u2026\u2026.(i)<\/p>\n<p>And <img decoding=\"async\" style=\"height: 29px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image050.png\" \/>\u00a0\u2026\u2026\u2026.(ii)<\/p>\n<p>From eq. (i), <img decoding=\"async\" style=\"height: 24px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image054.png\" \/><\/p>\n<p>Putting this value in eq. (ii),<\/p>\n<p><img decoding=\"async\" style=\"height: 29px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image055.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 21px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image056.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 19px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image057.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image058.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 41px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image058.png\" \/>\u00a0in <img decoding=\"async\" style=\"height: 24px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image054.png\" \/>,<\/p>\n<p><img decoding=\"async\" style=\"height: 49px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image059.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 45px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image060.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0The two points of intersections of circles (i) and (ii) are <img decoding=\"async\" style=\"height: 53px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image061.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 53px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image062.png\" \/>.<\/p>\n<p>Now, from eq. (i), <img decoding=\"async\" style=\"height: 28px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image063.png\" \/>\u00a0in first quadrant and from eq. (ii), <img decoding=\"async\" style=\"height: 35px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image064.png\" \/>\u00a0in first quadrant.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Required area OACBO = 2 x Area OAC = 2 (Area OAD + Area DAC)<\/p>\n<p>= <img decoding=\"async\" style=\"height: 80px; width: 287px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image065.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 80px; width: 236px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image066.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 88px; width: 436px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image067.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 53px; width: 348px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image068.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image069.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 53px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image070.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_82-2\"><\/span>NCERT Solutions class 12 Maths Exercise 8.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"3_Find_the_area_of_the_region_bounded_by_the_curves_and\"><\/span><strong>3. Find the area of the region bounded by the curves <\/strong><strong><img decoding=\"async\" style=\"height: 24px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image071.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 19px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image072.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong>Equation of the given curve is<\/p>\n<p><img decoding=\"async\" id=\"Picture 33\" style=\"height: 159px; width: 185px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image073.jpg\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 24px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image074.png\" \/>\u00a0\u00a0 \u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 24px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image075.png\" \/><\/p>\n<p>Here Vertex of the parabola is (0, 2).<\/p>\n<p>Equation of the given line is <img decoding=\"async\" style=\"height: 17px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image076.png\" \/>\u00a0\u00a0\u00a0\u2026.\u2026.(ii)<\/p>\n<p>Table of values for the line <img decoding=\"async\" style=\"height: 17px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image076.png\" \/><\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"width: .5in;\"><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image008.png\" \/><\/td>\n<td style=\"width: .5in;\">0<\/td>\n<td style=\"width: .5in;\">1<\/td>\n<td style=\"width: .5in;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: .5in;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image077.png\" \/><\/td>\n<td style=\"width: .5in;\">0<\/td>\n<td style=\"width: .5in;\">1<\/td>\n<td style=\"width: .5in;\">2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>We know that it is a straight line passing through the origin and having slope 1 i.e., making an angle of <img decoding=\"async\" style=\"height: 21px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image078.png\" \/>\u00a0with <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image079.png\" \/>\u00a0axis.<\/p>\n<p>Here also, Limits of integration area given to be <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image080.png\" \/>\u00a0to <img decoding=\"async\" style=\"height: 19px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image072.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Area bounded by parabola (i) namely <img decoding=\"async\" style=\"height: 24px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image081.png\" \/>\u00a0the <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image079.png\" \/>axis and the ordinates <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image080.png\" \/>\u00a0to <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image082.png\" \/>\u00a0is the area OACD and <img decoding=\"async\" style=\"height: 49px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image083.png\" \/><\/p>\n<p>=\u00a0 <img decoding=\"async\" style=\"height: 53px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image084.png\" \/>\u00a0= (9 + 6) \u2013 0 = 15 \u2026\u2026\u2026.(iii)<\/p>\n<p>Again Area bounded by parabola (ii) namely <img decoding=\"async\" style=\"height: 17px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image085.png\" \/>\u00a0the <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image079.png\" \/>axis and the ordinates <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image080.png\" \/>\u00a0to <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image082.png\" \/>\u00a0is the area OAB and <img decoding=\"async\" style=\"height: 49px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image086.png\" \/><\/p>\n<p>=\u00a0 <img decoding=\"async\" style=\"height: 53px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image087.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image088.png\" \/>\u00a0\u00a0\u00a0\u2026\u2026\u2026.(iii)<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Required area = Area OBCD = Area OACD \u2013 Area OAB<\/p>\n<p>= Area given by eq. (iii) \u2013 Area given by eq. (iv)<\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image089.png\" \/>\u00a0sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_82-3\"><\/span>NCERT Solutions class 12 Maths Exercise 8.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"4_Using_integration_find_the_area_of_the_region_bounded_by_the_triangle_whose_vertices_are_1_3_and_3_2\"><\/span><strong>4. Using integration, find the area of the region bounded by the triangle whose vertices are <\/strong><strong><img decoding=\"async\" style=\"height: 27px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image090.png\" \/><\/strong><strong>\u00a0(1, 3) and (3, 2).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong>Here, Vertices of triangle are A<img decoding=\"async\" style=\"height: 27px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image090.png\" \/>\u00a0B (1, 3) and<\/p>\n<p><img decoding=\"async\" id=\"Picture 35\" style=\"height: 149px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image091.jpg\" \/><\/p>\n<p>C (3, 2).<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Equation of the line is<\/p>\n<p><img decoding=\"async\" style=\"height: 47px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image092.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 51px; width: 184px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image093.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image094.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Area of <img decoding=\"async\" style=\"height: 17px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image095.png\" \/>\u00a0= Area bounded by line AB and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image079.png\" \/>axis<\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image096.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 200px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image097.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image098.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image099.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 59px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image100.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 48px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image101.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image102.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image103.png\" \/>\u00a0\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p>Again equation of line BC is <img decoding=\"async\" style=\"height: 41px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image104.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image105.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Area of trapezium BLMC = Area bounded by line BC and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image079.png\" \/>axis<\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image106.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image107.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 59px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image108.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 48px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image109.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 119px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image110.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 45px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image111.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image112.png\" \/>\u00a0= 5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u2026\u2026\u2026.(ii)<\/p>\n<p>Again equation of line AC is <img decoding=\"async\" style=\"height: 47px; width: 168px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image113.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image114.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Area of triangle ACM = Area bounded by line AC and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image079.png\" \/>axis<\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image115.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image116.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 59px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image117.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 48px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image118.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image119.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image120.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image121.png\" \/>\u00a0= 4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u2026\u2026\u2026.(iii)<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Required area = Area of <img decoding=\"async\" style=\"height: 17px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image095.png\" \/>\u00a0+ Area of Trapezium BLMC \u2013 Area of <img decoding=\"async\" style=\"height: 19px; width: 52px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image122.png\" \/><\/p>\n<p>= 3 + 5 \u2013 4 = 4 sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_82-4\"><\/span>NCERT Solutions class 12 Maths Exercise 8.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"5_Using_integration_find_the_area_of_the_triangular_region_whose_sides_have_the_equations_and\"><\/span><strong>5. Using integration, find the area of the triangular region whose sides have the equations <\/strong><strong><img decoding=\"async\" style=\"height: 21px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image123.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 19px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image124.png\" \/><\/strong><strong>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans. <\/strong>Equations of one side of triangle is<\/p>\n<p><img decoding=\"async\" id=\"Picture 36\" style=\"height: 277px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image125.jpg\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 21px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image126.png\" \/>\u00a0\u2026\u2026\u2026..(i)<\/p>\n<p>second line of triangle is <img decoding=\"async\" style=\"height: 21px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image127.png\" \/>\u00a0\u2026\u2026\u2026..(ii)<\/p>\n<p>third line of triangle is <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image128.png\" \/>\u00a0\u00a0\u2026\u2026\u2026.(iii)<\/p>\n<p>Solving eq. (i) and (ii), we get <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image080.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 21px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image129.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Point of intersection of lines (i) and (ii) is A (0, 1)<\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image128.png\" \/>\u00a0in eq. (i), we get <img decoding=\"async\" style=\"height: 21px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image130.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Point of intersection of lines (i) and (iii) is B (4, 9)<\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image128.png\" \/>\u00a0in eq. (i), we get <img decoding=\"async\" style=\"height: 21px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image131.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Point of intersection of lines (ii) and (iii) is C (4, 13)<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image023.png\" \/>\u00a0Area between line (ii) i.e., AC and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image079.png\" \/>axis<\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image132.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image133.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 53px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image134.png\" \/><\/p>\n<p>= 24 + 4 = 28 sq. units\u00a0 \u2026\u2026\u2026.(iv)<\/p>\n<p>Again Area between line (i) i.e., AB and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image079.png\" \/>axis<\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image132.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image135.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 33px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image136.png\" \/><\/p>\n<p>= 16 + 4 = 20 sq. units\u00a0 \u2026\u2026\u2026.(v)<\/p>\n<p>Therefore, Required area of <img decoding=\"async\" style=\"height: 19px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image137.png\" \/><\/p>\n<p>= Area given by (iv) \u2013 Area given by (v)<\/p>\n<p>= 28 \u2013 20 = 8 sq. units<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_82-5\"><\/span>NCERT Solutions class 12 Maths Exercise 8.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"6_Choose_the_correct_answer\"><\/span><strong>6. Choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Smaller area enclosed by the circle <img decoding=\"async\" style=\"height: 24px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image138.png\" \/>\u00a0and the line <img decoding=\"async\" style=\"height: 21px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image139.png\" \/>\u00a0is:<\/strong><\/p>\n<p><strong>(A) <img decoding=\"async\" style=\"height: 27px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image140.png\" \/>\u00a0\u00a0<\/strong><\/p>\n<p><strong>(B) <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image141.png\" \/>\u00a0\u00a0<\/strong><\/p>\n<p><strong>(C) <img decoding=\"async\" style=\"height: 19px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image142.png\" \/>\u00a0\u00a0<\/strong><\/p>\n<p><strong>(D) <img decoding=\"async\" style=\"height: 27px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image143.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><strong>Step I<\/strong>. Equation of circle is <img decoding=\"async\" style=\"height: 24px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image144.png\" \/>\u00a0\u2026\u2026.\u2026(i)<\/p>\n<p><img decoding=\"async\" id=\"Picture 39\" style=\"height: 155px; width: 134px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image145.jpg\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 28px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image146.png\" \/>\u00a0\u00a0\u00a0 \u2026\u2026\u2026(ii)<\/p>\n<p>Also, equation of the line is <img decoding=\"async\" style=\"height: 21px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image139.png\" \/>\u00a0\u00a0\u2026\u2026\u2026.(iii)<\/p>\n<p>Table of values<\/p>\n<table border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td style=\"width: .5in;\"><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image008.png\" \/><\/td>\n<td style=\"width: .5in;\">0<\/td>\n<td style=\"width: .5in;\">2<\/td>\n<\/tr>\n<tr>\n<td style=\"width: .5in;\"><img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image077.png\" \/><\/td>\n<td style=\"width: .5in;\">2<\/td>\n<td style=\"width: .5in;\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Therefore graph of equation (iii) is the straight line joining the points (0, 2) and (2, 0).<\/p>\n<p><strong>Step II<\/strong>. From the graph of circle (i) and straight line (iii), it is clear that points of intersections of circle (i) and straight line (iii) are A (2, 0) and B (0, 2).<\/p>\n<p><strong>Step III<\/strong>. Area OACB, bounded by circle (i) and coordinate axes in first quadrant = <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image147.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image148.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 53px; width: 171px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image149.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 235px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image150.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 136px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image151.png\" \/>\u00a0sq. units\u00a0\u00a0 \u2026\u2026\u2026.(iv)<\/p>\n<p><strong>Step IV<\/strong>. Area of triangle OAB, bounded by straight line (iii) and coordinate axes<\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image147.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image152.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 53px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image153.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 27px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image154.png\" \/>\u00a0= 2 sq. units\u00a0 \u2026\u2026\u2026.(v)<\/p>\n<p><strong>Step V<\/strong>. Required shaded area = Area OACB given by (iv) \u2013 Area of triangle OAB by (v)<\/p>\n<p>= <img decoding=\"async\" style=\"height: 27px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image155.png\" \/>\u00a0sq. units<\/p>\n<p>Therefore, option (B) is correct.<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_82-6\"><\/span>NCERT Solutions class 12 Maths Exercise 8.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"7_Choose_the_correct_answer\"><\/span><strong>7. Choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Area lying between the curves <img decoding=\"async\" style=\"height: 24px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image156.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 21px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image157.png\" \/>\u00a0is:<\/strong><\/p>\n<p><strong>(A) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image158.png\" \/>\u00a0\u00a0\u00a0<\/strong><\/p>\n<p><strong>(B) <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image159.png\" \/>\u00a0\u00a0\u00a0<\/strong><\/p>\n<p><strong>(C) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image160.png\" \/>\u00a0\u00a0\u00a0<\/strong><\/p>\n<p><strong>(D) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image161.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong>Equation of curve (parabola) is <img decoding=\"async\" style=\"height: 24px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image156.png\" \/>\u00a0\u2026..(i)<\/p>\n<p><img decoding=\"async\" id=\"Picture 41\" style=\"height: 128px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image162.jpg\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 25px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image163.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 32px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image164.png\" \/>\u00a0\u00a0\u00a0\u2026..(ii)<\/p>\n<p>Equation of another curve (line) is <img decoding=\"async\" style=\"height: 21px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image157.png\" \/>\u00a0\u2026..(iii)<\/p>\n<p>Solving eq. (i) and (iii), we get <img decoding=\"async\" style=\"height: 19px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image080.png\" \/>\u00a0or <img decoding=\"async\" style=\"height: 19px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image165.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 21px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image166.png\" \/>\u00a0or <img decoding=\"async\" style=\"height: 21px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image167.png\" \/><\/p>\n<p>Therefore, Points of intersections of circle (i) and line (ii) are O (0, 0) and A (1, 2).<\/p>\n<p>Now Area OBAM = Area bounded by parabola (i) and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image079.png\" \/>axis = <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image168.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image169.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 93px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image170.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image171.png\" \/>\u00a0\u00a0\u2026\u2026\u2026(iv)<\/p>\n<p>Also, Area <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image172.png\" \/>OAM = Area bounded by parabola (iii) and <img decoding=\"async\" style=\"height: 15px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image079.png\" \/>axis<\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image168.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image173.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 53px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image174.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 27px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image175.png\" \/>\u00a0\u00a0\u00a0\u2026\u2026\u2026(v)<\/p>\n<p>Now Required shaded area OBA = Area OBAM \u2013 Area of <img decoding=\"async\" style=\"height: 17px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image172.png\" \/>OAM<\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex8.2\/image176.png\" \/>\u00a0sq. units<\/p>\n<p>Therefore, option (B) is correct.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_82-7\"><\/span>NCERT Solutions class 12 Maths Exercise 8.2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 20 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_App_for_Class_12\"><\/span>CBSE App for Class 12<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download\u00a0NCERT Solutions for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions class 12 Maths Exercise 8.2 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 &#8230; <a title=\"NCERT Solutions class 12 Maths Exercise 8.2\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-8-2\/\" aria-label=\"More on NCERT Solutions class 12 Maths Exercise 8.2\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1432,281],"tags":[283,1342,321,216],"class_list":["post-4500","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-12","category-ncert-solutions","tag-cbse-study-material","tag-class-12","tag-mathematics","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions class 12 Maths Exercise 8.2 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Exercise 8.2 in PDF format for free download. 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