NCERT Solutions class 12 Maths Exercise 7.4

NCERT Solutions class 12 Maths Exercise 7.4 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.

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NCERT Solutions class 12 Maths Integrals

Integrate the following functions in Exercises 1 to 9.

1.  

Ans. Let I =

=  ……….(i)

Putting

 

 

  From eq. (i),

I =

=

=

---

2.  

Ans.

=

=

=

---

3.  

Ans.

=

=

=

---

4.  

Ans.

=

=

=

---

5.  

Ans. Let I =

=  ……….(i)

Putting

 

 

  From eq. (i),

I =

=

=

=

=

---

6.  

Ans. Let I =

=

=  ……….(i)

Putting

 

 

From eq. (i),

I =

=

=

 =

---

7.  

Ans. Let I =

=

=

=

Let I₁ =

Putting

 

 

 I₁ =  =  =  =

 I =

=

 I =  where

---

8.  

Ans. Let I =

= ……….(i)

Putting

 

 

  From eq. (i),

I =

=

=

=

---

9.  

Ans. Let I = ……….(i)

Putting

 

 

  From eq. (i),

I =

=

=

=

---

Integrate the following functions in Exercises 10 to 18.

10.  

Ans.

=

=

=

=

---

11.  

Ans.

=

=

=

[For making completing the squares]

=

=

=

=

=

=

---

12.  

Ans.

=

=

=

=

=

=

=

---

13.

Ans.

=

=

=

=

= 

= 

---

14.  

Ans.

=

=

=

=

=

= 

= 

---

15.  

Ans.

=

=

=

=

=

=

=

=

=

---

16.  

Ans. Let I =  ……….(i)

Putting

 

 

 From eq. (i),

I =

=

=

=

=

---

17.  

Ans. Let I =

=

=

=  …….(i)

Let I₁ =

=

Putting

 

I₁ =

=

=

=

=

Putting this value in eq. (i),

---

NCERT Solutions class 12 Maths Exercise 7.4

18.  

Ans. Let I =  ……….(i)

Let Linear = A  (Quadratic) + B

 ……(ii)

 

Comparing coefficients of  6A = 5

 A =

Comparing constants,

2A + B =

On solving, we get A = , B =

Putting the values of A and B in eq. (ii),

Putting this value of  in eq. (i),

I =

I =

 I =  ……….(iii)

Now I₁ =

Putting

 

 

I₁ =  =  =  ……….(iv)

Again I₂ =

=

=

=

=

=

=

=

=  ……….(v)

Putting values of I₁ and I₂ in eq. (iii),

I =

---

NCERT Solutions class 12 Maths Exercise 7.4

Integrate the following functions in Exercises 19 to 23.

19.

Ans. Let I =

=  ……….(i)

Let Linear = A  (Quadratic) + B

  ……(ii)

 

Comparing coefficients of  2A = 6  A = 3

Comparing constants, –9A + B = 7

On solving, we get A = 3, B = 34

Putting the values of A and B in eq. (ii),

Putting this value of  in eq. (i),

I =

I =

 I = ……….(iii)

Now I₁ =

Putting

 

 

I₁ =

=

=  =

=  ……….(iv)

Again I₂ =

=

=

=

=

=  ……….(v)

Putting values of I₁ and I₂ in eq. (iii),

I =

---

20.  

Ans. Let I =  ……….(i)

Let Linear = A  (Quadratic) + B

 ……(ii)

 

Comparing coefficients of  –2A = 1  A =

Comparing constants, 4A + B = 2

On solving, we get A = B = 4

Putting the values of A and B in eq. (ii),

Putting this value of  in eq. (i),

I =

I =

 I =  ……….(iii)

Now I₁ =

Putting

 

 

 I₁ =  =

=  =

= …….(iv)

Again I₂ =

=

=

=

=

=

= ……….(v)

Putting values of I₁ and I₂ in eq. (iii),

I =

---

21.  

Ans. Let I =

Let Linear = A  (Quadratic) + B

 ……(ii)

 

Comparing coefficients of  2A = 1  A =

Comparing constants, 2A + B = 2

On solving, we get A = B = 1

Putting the values of A and B in eq. (ii),

Putting this value of  in eq. (i),

I =

I =

 I =  ……….(iii)

Now I₁ =

Putting

 

 

I₁ =  =

=  =

=  ……….(iv)

Again I₂ =

=

=

=

=  ……….(v)

Putting values of I₁ and I₂ in eq. (iii),

I =

---

22.  

Ans. Let I =  ……….(i)

Let Linear = A  (Quadratic) + B

 ……(ii)

 

Comparing coefficients of  2A = 1

 A =

Comparing constants, –2A + B = 3

On solving, we get A = B = 4

Putting the values of A and B in eq. (ii), 

Putting this value of  in eq. (i),

I =

I =

 I =  ……….(iii)

Now I₁ =

Putting

 

 

I₁ =  =

=  ……….(iv)

Again I₂ =

=

=

= ……….(v)

Putting values of I₁ and I₂ in eq. (iii),

I =

---

NCERT Solutions class 12 Maths Exercise 7.4

23.  

Ans. Let I = ……….(i)

Let Linear = A  (Quadratic) + B

 

  ……(ii)

 

Comparing coefficients of  2A = 5  A =

Comparing constants, 4A + B = 2

On solving, we get A = B =

Putting the values of A and B in eq. (ii),

Putting this value of  in eq. (i),

I =

I =

 I = ……….(iii)

Now I₁ =

Putting

 

 

I₁ =

=

=  =

= ……….(iv)

Again I₂ =

=

=

=

=  ……….(v)

Putting values of I₁ and I₂ in eq. (iii),

I =

---

NCERT Solutions class 12 Maths Exercise 7.4

Choose the correct answer in Exercise 24 and 25.

24.  equals

(A)  

(B)  

(C)  

(D)

Ans.

=

=

=

Therefore, option (B) is correct.

---

25.  equals

(A)

(B)

(C)  

(D)

Ans. Let I =

=

=

=

=

=

=

=

=

Therefore, option (B) is correct.

NCERT Solutions class 12 Maths Exercise 7.4

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

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