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int(-pi)^(pi) ( sin^(4) x )/( sin^(4)x +...

`int_(-pi)^(pi) ( sin^(4) x )/( sin^(4)x +cos^(4) x )dx` is equal to

A

`(pi)/(4)`

B

`(pi)/(2)`

C

`(3pi)/(2)`

D

`pi`

Text Solution

Verified by Experts

The correct Answer is:
D
`"Let "I=2int_(0)^(pi)(sin^(4)x)/(sin^(4)x+cos^(4)x)dx`
`=4int_(0)^(pi//2)(sin^(4)x)/(sin^(4)x+cos^(4)x)dx" ….(i)"`
`rArr" "I=4 int_(0)^(pi//2)(cos^(4)x)/(sin^(4)x+cos^(4)x)dx" …..(ii)"`
On adding equations (i) and (ii), we get
`2I=4int_(0)^(pi//2)1.dx=2pi" "rArr" "I=pi`
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