# Exercise 7.11

By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19.(Ex 7.11 integration ncert maths solution class 12)

Question 1:

Solution : Let

Adding (1) and (2), we have

Question 2:

Solution: Let

Adding (1) and (2), we have

Question 3:

Solution:Let

Adding (1) and (2), we have

Question4:

Solution: Let

Question 5:

Solution: Let

Question 6:

Solution: Let

Question 7:

Solution: Let

Question 8:

Solution: Let

Using property:

Question 9:

Soltuion: Let

Question 10:

Solution: Let

Using property, , we have

Adding (1) and (2), we have

Question 11:

Solution: Let

Here, , therefore, is an even function.

We know that if is an even function, then

Question 12:

Solution:- Let

Question 13:

Solution: Let

Here, , therefore, is an odd function.

We know that if is an even function, then

Therefore,

Question 14:

Solution: Let

We know that,

Here,

Now,

Question 15:

Solution : Let

Adding (1) and (2), we have

Question 16:

Solution : Let

Adding (1) and (2), we have

We know that,

Here,

Adding (4) and (5), we have

Let

Question 17:

Solution : Let

Using property: , we have

Adding (1) and (2), we have

Question 18:

Solution :

Question 19: Show that if and are defined as and

Solution : Let

Adding (1) and (2), we have

Question 20: The value of is

(A) 0

(B) 2

(C)

(D) 1

Solution : The correct answer is (C)

Let

We know that,

Therefore,

Hence, the correct answer is (C).

Question 21: The value of is

(A) 2

(B)

(C) 0

(D)

Solution: The correct answer is (C)

Let

Hence, the correct answer is (C).

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