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Prove that int(0)^((pi)/(2)) log ( tan x...

Prove that `int_(0)^((pi)/(2)) log ( tan x ) dx = 0 `

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Knowledge Check

  • int_(0)^((pi)/(2)) log (cotx)dx is :

    A
    0
    B
    `(pi)/(4)`
    C
    `(pi)/(2)`
    D
    `pi`.

  • The value of int_(0)^((pi)/(2)) (dx)/( 1+ tan x) is

    A
    `pi`
    B
    `(pi)/( 2)`
    C
    `(pi)/(4)`
    D
    0

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    Prove that int_(0)^(pi/4)log(1+tanx)dx=(pi)/(8) log2.

    Provethat int_(0)^((pi)/(2))(dx)/(1+tanx)=(pi)/(4)

    By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/4)log (1 tan x) dx

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