# EXERCISE 7.3(Integration)

Find the integrals of the functions in Exercises 1 to 22:(Ex 7.3 integration ncert maths solution class 12)

Question 1:

Solution: Let

Using formula

Question 2:

Question: Let

Question 3:

Solution: Let

Using the identity

given expression can be written as

Question 4:

Solution: Let

Let

Substitute ,

Question 5:

Solution: Let

Let

Substitute ,

Question 6:

Solution: Let

Using the identity , given expression can be written as

Question 7:

Solution: LetÂ  .

Using the identity

,

given expression can be written as

Integration of given expression is

Question 8:

Solution: Let .

Using the identities

and

Question 9: .

Solution: Let .

Using the identity

and

given expression can be written as

Question 10: .

Solution: Let .

Question 11:

Solution: Let

Question 12:

Solution: Let I=.

Question 13: .

Solution: Let .

Question 14:

Solution: Let .

We know that

.

.

We can apply the identity

,

Let

Question 15: .

Solution: Let .

Let

Question 16: .

Solution: Let .

Let

Question 17: .

Solution:Let .

Question18: .

Solution: Let .

By applying the identity

Question 19: .

Solution: Let .

We can apply the identity

,

Let

Question 20: .

Solution:Let .

Let

Question 21: .

Solution: Let .

Question 22: .

Solution: Let .

Given expression can be written as

Question 23: is equal to

(A)

(B)

(C)

(D)

Solution: option A is the correct answer.

Let .

Therefore, option (A )is the correct answer.

Question 24: Solve the following: equals

(A)

(B)

(C)

(D)

Solution: option A is the correct answer.

Let .

Let

Integration of given expression is

Therefore, option (B) is the correct answer.

Ex 7.2 integration ncert solution maths class 12