# NCERT solution class 12 chapter 1 Integrals exercise 1.11 mathematics part 2

## EXERCISE 1.11

#### 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 7:  #### Question 8:  #### Question 9:  #### 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.

#### Question 21:

The value of is

A. 2

B. C. 0

D.   Adding (1) and (2), we obtain Hence, the correct answer is C.

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