{"id":4463,"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-7-1\/"},"modified":"2018-05-07T14:20:14","modified_gmt":"2018-05-07T08:50:14","slug":"ncert-solutions-class-12-maths-exercise-7-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-7-1\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 7.1"},"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-7-1\/#NCERT_Solutions_class_12_Maths_Integrals\" >NCERT Solutions class 12 Maths 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-7-1\/#NCERT_Solutions_class_12_Maths_Exercise_71\" >NCERT Solutions class 12 Maths Exercise 7.1<\/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-7-1\/#Evaluate_the_following_integrals_in_Exercises_17_to_20\" >Evaluate the following integrals in Exercises 17 to 20.<\/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-7-1\/#NCERT_Solutions_class_12_Maths_Exercise_71-2\" >NCERT Solutions class 12 Maths Exercise 7.1<\/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-7-1\/#21_Choose_the_correct_answer\" >21. 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-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-7-1\/#NCERT_Solutions_class_12_Maths_Exercise_71-3\" >NCERT Solutions class 12 Maths Exercise 7.1<\/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-7-1\/#22_Choose_the_correct_answer\" >22. 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-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-7-1\/#NCERT_Solutions_class_12_Maths_Exercise_71-4\" >NCERT Solutions class 12 Maths Exercise 7.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-7-1\/#CBSE_App_for_Students\" >CBSE App for Students<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Exercise 7.1 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-integrals\/1291\/ncert-solutions\/5\/\">NCERT solutions for\u00a0Integrals\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 7.1\" width=\"195\" height=\"250\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Integrals\"><\/span>NCERT Solutions class 12 Maths Integrals<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p style=\"text-align: justify;\"><strong>Find an antiderivative (or integral) of the following functions by the method of inspection in Exercises 1 to 5.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>1. \u00a0<img decoding=\"async\" style=\"height: 19px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image001.png\" \/><\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image002.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image003.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image005.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 45px; width: 153px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image006.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image007.png\" \/>\u00a0 An anti-derivative of <img decoding=\"async\" style=\"height: 19px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image001.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 41px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image008.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>2. <img decoding=\"async\" style=\"height: 19px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image009.png\" \/><\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image002.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image010.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image011.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 45px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image012.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image007.png\" \/>\u00a0 An anti-derivative of <img decoding=\"async\" style=\"height: 19px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image009.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image013.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>3. <img decoding=\"async\" style=\"height: 21px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image014.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image002.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image015.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 90px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image016.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 45px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image017.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image007.png\" \/>\u00a0An anti-derivative of <img decoding=\"async\" style=\"height: 21px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image014.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 41px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image018.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>4. <img decoding=\"async\" style=\"height: 29px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image019.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image002.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 327px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image020.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image021.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 45px; width: 187px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/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\/Ex7.1\/image007.png\" \/>\u00a0An anti-derivative of <img decoding=\"async\" style=\"height: 29px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image023.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 41px; width: 85px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image024.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>5. <img decoding=\"async\" style=\"height: 21px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image025.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image002.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image003.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/><img decoding=\"async\" style=\"height: 41px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image005.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 45px; width: 153px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image006.png\" \/> \u2026..(i)<\/p>\n<p>Again <img decoding=\"async\" style=\"height: 41px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image026.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 45px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image027.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 45px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image028.png\" \/>\u00a0 [Multiplying both sides by <img decoding=\"async\" style=\"height: 17px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image029.png\" \/>] \u2026\u2026\u2026.(ii)<\/p>\n<p>Adding eq. (i) and (ii), we get<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 45px; width: 305px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image030.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 45px; width: 239px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image031.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image007.png\" \/>\u00a0An anti-derivative of <img decoding=\"async\" style=\"height: 21px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image025.png\" \/>\u00a0is <img decoding=\"async\" style=\"height: 41px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image032.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>Evaluate the following integrals in Exercises 6 to 11.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>6. \u00a0<img decoding=\"async\" style=\"height: 29px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image033.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 29px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image033.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image034.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image035.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image036.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 51px; width: 200px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image037.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>7. <img decoding=\"async\" style=\"height: 45px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image038.png\" \/><\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 45px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image038.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 51px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image039.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 29px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image040.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 29px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image041.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 44px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image042.png\" \/> <img decoding=\"async\" style=\"height: 51px; width: 183px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image043.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>8. <img decoding=\"async\" style=\"height: 29px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image044.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 29px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image044.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image045.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 175px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image046.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image047.png\" \/>\u00a0where <img decoding=\"async\" style=\"height: 24px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image048.png\" \/>\u00a0is the constant of integration.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>9. <img decoding=\"async\" style=\"height: 29px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image049.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 29px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image049.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image050.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image051.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image052.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>10. <img decoding=\"async\" style=\"height: 51px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image053.png\" \/><\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 51px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image053.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 56px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image054.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image055.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image056.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 44px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image057.png\" \/><strong>\u00a0<\/strong><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>11. <img decoding=\"async\" style=\"height: 44px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image058.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 44px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image058.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image059.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image060.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image061.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 171px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image062.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image063.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>Evaluate the following integrals in Exercises 12 to 16.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>12. <img decoding=\"async\" style=\"height: 47px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image064.png\" \/><\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 47px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image064.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 64px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image065.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 168px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image066.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image067.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 39px; width: 191px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image068.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 75px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image069.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 75px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image070.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 132px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image071.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>13. <img decoding=\"async\" style=\"height: 44px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image072.png\" \/><\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 44px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image073.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image074.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 53px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image075.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image076.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image077.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image078.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>14. <img decoding=\"async\" style=\"height: 29px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image079.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 29px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image079.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 32px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image080.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image081.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 39px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image082.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image083.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 75px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image084.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 44px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image085.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>15. <img decoding=\"async\" style=\"height: 29px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image086.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 29px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image086.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 39px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image087.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image088.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 39px; width: 193px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image089.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 75px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image090.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 75px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image091.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image092.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>16. <img decoding=\"async\" style=\"height: 29px; width: 148px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image093.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 29px; width: 148px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image093.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 192px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image094.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 191px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image095.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image096.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 21px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image097.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_71\"><\/span>NCERT Solutions class 12 Maths Exercise 7.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Evaluate_the_following_integrals_in_Exercises_17_to_20\"><\/span><strong>Evaluate the following integrals in Exercises 17 to 20.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>17.\u00a0 <img decoding=\"async\" style=\"height: 32px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image098.png\" \/><\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 32px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image098.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 39px; width: 205px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image099.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 75px; width: 187px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image100.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 75px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image101.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 157px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image102.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>18. <img decoding=\"async\" style=\"height: 29px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image103.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 29px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image103.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 163px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image104.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image105.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 17px; width: 102px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image106.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>19. <img decoding=\"async\" style=\"height: 44px; width: 90px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image107.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 44px; width: 90px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image107.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 81px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image108.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image109.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image110.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image111.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image112.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 17px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image113.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>20.\u00a0 <img decoding=\"async\" style=\"height: 41px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image114.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 41px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image114.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 148px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image115.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image116.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 29px; width: 193px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image117.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 19px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image118.png\" \/><\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_71-2\"><\/span>NCERT Solutions class 12 Maths Exercise 7.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"21_Choose_the_correct_answer\"><\/span><strong>21. Choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>The anti derivative of <img decoding=\"async\" style=\"height: 48px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image119.png\" \/>\u00a0equals.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 41px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image120.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 41px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image121.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 41px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image122.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 41px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image123.png\" \/><\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 48px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image124.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 51px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image125.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 39px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image126.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 75px; width: 116px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image127.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 75px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image128.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image129.png\" \/><\/p>\n<p>Therefore, option (C) is correct.<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_71-3\"><\/span>NCERT Solutions class 12 Maths Exercise 7.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"22_Choose_the_correct_answer\"><\/span><strong>22. Choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p style=\"text-align: justify;\"><strong>If <img decoding=\"async\" style=\"height: 41px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image130.png\" \/>\u00a0such that <img decoding=\"async\" style=\"height: 28px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image131.png\" \/>\u00a0Then <img decoding=\"async\" style=\"height: 28px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image132.png\" \/>\u00a0is:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 41px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image133.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 41px; width: 90px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image134.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 41px; width: 90px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image135.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 41px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image136.png\" \/><\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 45px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image137.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image138.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image139.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 44px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image140.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0 <img decoding=\"async\" style=\"height: 41px; width: 124px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image141.png\" \/>\u00a0\u2026\u2026\u2026.(i)<\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image142.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image143.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image144.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 17px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image004.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image145.png\" \/><\/p>\n<p>Putting <img decoding=\"async\" style=\"height: 41px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image145.png\" \/>\u00a0in eq. (i),<\/p>\n<p><img decoding=\"async\" style=\"height: 41px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex7.1\/image146.png\" \/><\/p>\n<p>Therefore, option (A) is correct.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_71-4\"><\/span>NCERT Solutions class 12 Maths Exercise 7.1<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 13 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_Students\"><\/span>CBSE App for Students<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 7.1 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 7.1\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-7-1\/\" aria-label=\"More on NCERT Solutions class 12 Maths Exercise 7.1\">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-4463","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 7.1 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Exercise 7.1 in PDF format for free download. 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