# NCERT solution class 12 chapter 1 Integrals exercise 1.10 mathematics part 2

## EXERCISE 1.10

#### Question 1:  When x = 0, t = 1 and when x = 1, t = 2 #### Question 2:  Also, let  #### Question 3:  Also, let x = tanθ ⇒ dx = sec2θ dθ

When x = 0, θ = 0 and when = 1,  Takingθas first function and sec2θ as second function and integrating by parts, we obtain #### Question 4:  Let + 2 = t2 ⇒ dx = 2tdt

When x = 0, and when = 2, = 2 #### Question 5:  Let cos x = t ⇒ −sinx dx = dt

When x = 0, = 1 and when  #### Question 6:  Let ⇒ dx = dt #### Question 7:  Let x + 1 = ⇒ dx = dt

When x = −1, = 0 and when x = 1, = 2 #### Question 8:  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  Let cotθ = t ⇒ −cosec2θ dθdt 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 cos x Integrating by parts, we obtain Hence, the correct answer is B.

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