# NCERT Class 12-Mathematics: Exemplar Chapter – 7 Integrals Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 8**:

Find

**Answer**:

Dividing numerator and denominator by , we have

Put so that . Then

**Question 9**:

Evaluate as a limit of sums.

**Answer**:

Here

Now, we have

Note that

Therefore,

**Question 10**:

Evaluate

**Answer**:

We have

Adding (1) and (2) , we get

**Question 11**:

Find

**Answer**:

We have

Adding (1) and (2) , we get

Hence

**Question 12**:

Find

**Answer**:

We have