The Secure way of Learning

Welcome! Guest

CBSE And NCERT Solutions:

# NCERT Solutions for Class 12 Mathematics-II english Medium 7. Integrals

Page 4 of 12

## 7. Integrals

#### Exercise 7.4

Exercise 7.4

Integrate the following functions in Exercises 1 to 23.

Ques.1.

Ans. Let I =

……….(i)

Putting

From eq. (i),

I =

Ans.

Ans.

Ans.

Ans. Let I =

……….(i)

Putting

From eq. (i),

I =

Ans. Let I =

……….(i)

Putting

From eq. (i),

I =

=

Ans. Let I =

Let I1 =

Putting

I1 =  =  =  =

I =

I =  where

### Ques.8.

Ans. Let I =

……….(i)

Putting

From eq. (i),

I =

Ques.9.

Ans. Let I = ……….(i)

Putting

From eq. (i),

I =

### Ques.10.

Ans.

Ques.11.

Ans.

[For making completing the squares]

Ques.12.

Ans.

Ques.13.

Ans.

=

=

Ques.14.

Ans.

=

=

Ques.15.

Ans.

Ques.16.

Ans. Let I =  ……….(i)

Putting

From eq. (i),

I =

Ques.17.

Ans. Let I =

…….(i)

Let I1 =

Putting

I1 =

Putting this value in eq. (i),

Ques.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 =

Ques.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 =

Ques.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 =

Ques.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 =

Ques.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 =

Ques.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 =

Choose the correct answer in Exercise 24 and 25.

Ques.24.  equals

(A)

(B)

(C)

(D)

Ans.

hance, option (B) is correct.

Ques.25.  equals

(A)

(B)

(C)

(D)

Ans. Let I =

www.atpeducation.com

www.atpeducation.com

Page 4 of 12

## Topic Lists:

##### NCERT Solutions⇒Class 12th ⇒ Mathematics-II ⇒ Chapter 7. Integrals:

See other sub-topics of this chapter: