# NCERT Class 12-Mathematics: Exemplar Chapter –7 Integrals Part 3

Doorsteptutor material for IEO Class-7 is prepared by world's top subject experts: fully solved questions with step-by-step explanation- practice your way to success.

**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