## NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Ex 7.11

#### Question 1:

Adding (1) and (2), we obtain

#### Question 2:

Adding (1) and (2), we obtain

#### Question 3:

Adding (1) and (2), we obtain

#### Question 4:

Adding (1) and (2), we obtain

#### Question 5:

It can be seen that (x + 2) ≤ 0 on [−5, −2] and (x + 2) ≥ 0 on [−2, 5].

#### Question 6:

It can be seen that (x − 5) ≤ 0 on [2, 5] and (x − 5) ≥ 0 on [5, 8].

#### Question 10:

Adding (1) and (2), we obtain

#### Question 11:

As sin(−x) = (sin (−x))2 = (−sin x)2 = sin2x, therefore, sin2is an even function.
It is known that if f(x) is an even function, then

#### Question 12:

Adding (1) and (2), we obtain

#### Question 13:

As sin(−x) = (sin (−x))7 = (−sin x)7 = −sin7x, therefore, sin2is an odd function.
It is known that, if f(x) is an odd function, then

#### Question 14:

It is known that,

#### Question 15:

Adding (1) and (2), we obtain

#### Question 16:

Adding (1) and (2), we obtain
sin (π − x) = sin x
Adding (4) and (5), we obtain
Let 2x = t ⇒ 2dx = dt
When x = 0, = 0 and when
x=π2, t=π∴
I=12∫0πlog sin tdt-π2log 2
⇒I=I2-π2log 2       [from 3]
⇒I2=-π2log 2
⇒I=-πlog 2

#### Question 17:

It is known that,
Adding (1) and (2), we obtain

#### Question 18:

It can be seen that, (x − 1) ≤ 0 when 0 ≤ x ≤ 1 and (x − 1) ≥ 0 when 1 ≤ x ≤ 4

#### Question 19:

Show that if f and g are defined as and

Adding (1) and (2), we obtain

#### Question 20:

The value of is
A. 0
B. 2
C. π
D. 1

It is known that if f(x) is an even function, then  and
if f(x) is an odd function, then
Hence, the correct answer is C.

The value of is
A. 2
B.
C. 0
D.