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int0^pi (xtanx)/(secx+tanx)dx...

`int_0^pi (xtanx)/(secx+tanx)dx`

A

`(pi^(2))/4`

B

`(pi^(2))/2`

C

`(3pi^(2))/2`

D

`(pi^(2))/3`

Text Solution

AI Generated Solution

To solve the integral \( I = \int_0^\pi \frac{x \tan x}{\sec x + \tan x} \, dx \), we can follow these steps: ### Step 1: Simplify the integrand We start with the integrand: \[ \frac{x \tan x}{\sec x + \tan x} \] We know that: ...
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Knowledge Check

  • int_(0)^(pi)(x tanx)/(secx+cosx)dx is

    A
    `(pi^(2))/4`
    B
    `(pi^(2))/2`
    C
    `(3pi^(2))/2`
    D
    `(pi^(2))/3`

  • int(1)/(secx+tanx)dx=

    A
    `(1)/(sec)+c`
    B
    `secx+log(secx+tanx)+c`
    C
    `cosx+log(cosx-cotx)+c`
    D
    `log(secx)+c`

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