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Evaluate : int0^(pi/2)(xsinxcosx)/(sin^4...

Evaluate : `int_0^(pi/2)(xsinxcosx)/(sin^4x+cos^4x)\ dx`

A

`(pi^(2))/2`

B

`(pi^(2))/4`

C

`(pi^(2))/8`

D

`(pi^(2))/16`

Text Solution

AI Generated Solution

To evaluate the integral \[ I = \int_0^{\frac{\pi}{2}} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x} \, dx, \] we can use a symmetry property of definite integrals. Let's proceed step by step. ...
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