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Evaluate: int0^(pi//4)"log"(1+"t a n x")...

Evaluate: `int_0^(pi//4)"log"(1+"t a n x")dx`

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To evaluate the integral \( I = \int_0^{\frac{\pi}{4}} \log(1 + \tan x) \, dx \), we can use a property of definite integrals. ### Step 1: Set Up the Integral Let: \[ I = \int_0^{\frac{\pi}{4}} \log(1 + \tan x) \, dx \] ...
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Knowledge Check

  • The value of int_(0)^(pi//4) log (1+ tan x) dx is

    A
    `(1)/(2) pi log 8`
    B
    `(1)/(8) pi log 2`
    C
    `(1)/(4) pi log 2`
    D
    None of these
  • int_0^(pi//4) log(1+ tan x)dx is equal to

    A
    `pi/8 log_e2`
    B
    `pi/4 log_2 e`
    C
    `pi/4 log_e2`
    D
    `pi/8 log_e(1/2)`
  • int_0^(pi//4)log(1+tanx)dx is equal to

    A
    `pi/8log_e2`
    B
    `pi/4log_2e`
    C
    `pi/4log_e2`
    D
    `pi/8log_e(1/2)`
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