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int (-pi)^(pi) (sin^(4)x)/(sin^(2) x + c...

` int _(-pi)^(pi) (sin^(4)x)/(sin^(2) x + cos^(4) x )dx ` is equal to

A

`( pi)/(4)`

B

`( pi)/(2)`

C

`(3pi)/( 2)`

D

`pi`

Text Solution

Verified by Experts

Let `I= 2 int_(0)^(pi) ( sin^(4) x )/( sin^(4) x + cos ^(4) x ) dx `
`= 4 int_(0)^(pi//2)( sin^(4) x)/( sin^(4) x+ cos ^(4) x ) dx ` ...(i)
`rArr I = 4 int_(0)^(pi//2) ( cos^(4))/( sin^(4)x + cos^(4) x ) ` ....(ii) On adding equations (i) and (ii) , we get
`2I = 4 int_(0) ^(pi//2) 1. dx = 2pi rArr I = pi`
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