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If int (0)^(pi//2) sin^(6) dx = (5pi)/32...

If `int _(0)^(pi//2) sin^(6) dx = (5pi)/32 ,` then the value of
` int _(-pi)^(pi) (sin ^(6) x + cos^(6)x)dx` is

A

`(5pi)/8`

B

`(5pi)/16`

C

`(5pi)/2`

D

`(5pi)/4`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `int_(-pi)^(pi)(sin^(6)x+cos^(6)x)dx`
`=2int_(0)^(pi)(sin^(6)x+cos^(6)x)dx`
`=4int_(0)^(pi//2)sin^(6)x dx+4int_(0)^(pi//2)cos^(6)((pi)/(2)-x)dx`
`8int_(0)^(pi//2)sin^(6)xdx=8xx(5pi)/(32)=(5pi)/(4)" [given]"`
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