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