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If int(0)^(1) tan^(-1) x dx = p , then t...

If `int_(0)^(1) tan^(-1) x` dx = p , then the value of `int_(0)^(1) tan^(-1)((1-x)/(1 +x))` dx is

A

`pi/4+p`

B

`pi/4-p`

C

`1+p`

D

`1-p`

Text Solution

Verified by Experts

The correct Answer is:
B
`int_(0)^(1)tan^(-1)((1-x)/(1+x))dx = int_(0)^(1)[tan^(-1)(1)-tan^(-1)(x)]dx`
`= int_(0)^(1)(pi)/(4)dx = int_(0)^(1) tan^(-1)(x)dx = (pi)/(4)-p`
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