# NCERT Class 12-Mathematics: Exemplar Chapter – 7 Integrals Part 5 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 18**:

Find

**Answer**:

Integrating by parts, we have

Now

Thus,

Therefore,

**Question 19**:

Evaluate

**Answer**:

We can redefine

Therefore,

## Objective Type Questions

### Choose the Correct Answer from the Given Four Options in Each of the Examples from 20 to 30

**Question 20**:

is equal to

(A)

(B)

(C)

(D)

**Answer**:

(A) Is the correct answer since

. Here .

**Question 21**:

(A)

(B)

(C)

(D)

**Answer**:

(C) Is the correct answer, since

**Question 22**:

If then

(A)

(B)

(C)

(D)

**Answer**:

C) is the correct answer,

Since differentiating both sides, we have

giving . Comparing coefficients on both sides, we get and . This verifies