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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) = ((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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Knowledge Check

  • int_(0)^(1)x tan^(-1)x dx=

    A
    `(pi)/(4)-(log 2)`
    B
    `(pi)/(4)-(1)/(2)`
    C
    `(pi)/(4)-1`
    D
    `(pi)/(4)+(log 2)`

  • int_(0)^(1) x tan^(-1) x " "dx =

    A
    `pi/4 + 1/2`
    B
    `pi/4 - 1/2`
    C
    `1/2- pi/4`
    D
    `(-pi)/4-1/2`

  • int _(0) ^(1) x tan ^(-1) x dx =

    A
    `(pi)/(4) +(1)/(2)`
    B
    `(pi)/(4)-(1)/(2)`
    C
    `(1)/(2)-(pi)/(4)`
    D
    `-(pi)/(4)-(1)/(2)`

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