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Prove that int(a)^(b) f(x)dx= int(a)^(b)...

Prove that `int_(a)^(b) f(x)dx= int_(a)^(b) f (a+b-x)dx" hence evaluate " int_(0)^(pi/4) log(1+tan x)dx`.

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Prove that int_(0)^(a)(x)dx = int_(0)^(a) f(a-x)dx and hence evaluate int_(0)^(pi/4)log (1 + tan x)dx .

Evaulate int_(0)^(pi//4)log(1+tanx)dx .

Knowledge Check

  • int_0^(pi//2) log(tan x)dx =

    A
    `pi/2`
    B
    `0`
    C
    `1`
    D
    `pi/4`

  • int_(0)^(pi//2) log sin x dx =

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

  • int_0^(pi//2) log(tan x) dx is :

    A
    `int_0^(pi//2) log cot x dx`
    B
    `(-pi)/2 log 2`
    C
    `pi/2 log 2`
    D
    0

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