NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Ex 7.10

NCERT Solutions for Class 12 Maths Chapter 7 – Integrals Ex 7.10

Page No 340:

Question 1:

Answer:

When x = 0, t = 1 and when x = 1, t = 2

Question 2:

Answer:

Also, let 

Question 3:

Answer:

Also, let x = tanθ ⇒ dx = sec²θ dθ

When x = 0, θ = 0 and when x = 1, 

Takingθas first function and sec²θ as second function and integrating by parts, we obtain

Question 4:

Answer:

Let x + 2 = t² ⇒ dx = 2tdt

When x = 0,  and when x = 2, t = 2

Question 5:

Answer:

Let cos x = t ⇒ −sinx dx = dt

When x = 0, t = 1 and when

Question 6:

Answer:

Let ⇒ dx = dt

Question 7:

Answer:

Let x + 1 = t ⇒ dx = dt

When x = −1, t = 0 and when x = 1, t = 2

Question 8:

Answer:

Let 2x = t ⇒ 2dx = dt

When x = 1, t = 2 and when x = 2, t = 4

Question 9:

The value of the integral  is

A. 6

B. 0

C. 3

D. 4

Answer:

Let cotθ = t ⇒ −cosec2θ dθ= dt

Hence, the correct answer is A.

Question 10:

If 

A. cos x + x sin x

B. x sin x

C. x cos x

D. sin x + x cos x

Answer:

Integrating by parts, we obtain

Hence, the correct answer is B.