NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Ex 7.11
Page No 347:
Question 1:
Answer:
Adding (1) and (2), we obtain
Question 2:
Answer:
Adding (1) and (2), we obtain
Question 3:
Answer:
Adding (1) and (2), we obtain
Question 4:
Answer:
Adding (1) and (2), we obtain
Question 5:
Answer:
It can be seen that (x + 2) ≤ 0 on [−5, −2] and (x + 2) ≥ 0 on [−2, 5].
Question 6:
Answer:
It can be seen that (x − 5) ≤ 0 on [2, 5] and (x − 5) ≥ 0 on [5, 8].
Question 7:
Answer:
Question 8:
Answer:
Question 9:
Answer:
Question 10:
Answer:
Adding (1) and (2), we obtain
Question 11:
Answer:
As sin2 (−x) = (sin (−x))2 = (−sin x)2 = sin2x, therefore, sin2x is an even function.
It is known that if f(x) is an even function, then 
Question 12:
Answer:
Adding (1) and (2), we obtain
Question 13:
Answer:
As sin7 (−x) = (sin (−x))7 = (−sin x)7 = −sin7x, therefore, sin2x is an odd function.
It is known that, if f(x) is an odd function, then 
Question 14:
Answer:
It is known that,
Question 15:
Answer:
Adding (1) and (2), we obtain
Question 16:
Answer:
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, t = 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:
Answer:
It is known that, 
Adding (1) and (2), we obtain
Question 18:
Answer:
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 
if f and g are defined as and Answer:
Adding (1) and (2), we obtain
Question 20:
The value of 
is
is
A. 0
B. 2
C. π
D. 1
Answer:
It is known that if f(x) is an even function, then 
and
and
if f(x) is an odd function, then 
Hence, the correct answer is C.
Question 21:
The value of 
is
is
A. 2
B. 
C. 0
D. 
Answer:
Adding (1) and (2), we obtain
Hence, the correct answer is C.
