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Chapter 7 Integrals Ex 7.10 Solutions

Question - 1 : -

Answer - 1 : -

When x =0, t = 1 and when x = 1, t =2

Question - 2 : -

Answer - 2 : -

Also, let 

Question - 3 : -

Answer - 3 : -

Also, let x =tanθ ⇒ dx =sec2θ dθ

When x =0, θ = 0 and when x = 1, 

Taking θ as firstfunction and sec2θ  as second function and integratingby parts, we obtain

Question - 4 : -

Answer - 4 : -

Let x + 2= t2 ⇒ dx = 2tdt

When x =0,  and when x =2, t = 2

Question - 5 : -

Answer - 5 : -

Let cos x = t ⇒ −sinx dx = dt

When x =0, t = 1 and when

Question - 6 : -

Answer - 6 : -

Let ⇒ dx = dt

Question - 7 : -

Answer - 7 : -

Let x + 1= t ⇒ dx = dt

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

Question - 8 : -

Answer - 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

Answer - 9 : -

Let cotθ = t ⇒ −cosec2θ dθ= dt

Hence, the correct answeris 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 - 10 : -

Integrating by parts, weobtain

Hence, the correct answeris B.

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