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int (0)^(2pi) sin^(6) x cos^(5) x dx is...

` int _(0)^(2pi) sin^(6) x cos^(5) x dx ` is equal to

A

`2pi`

B

`pi//2`

C

0

D

`-pi`

Text Solution

Verified by Experts

The correct Answer is:
C
Let ` l = int_(0)^(2pi)sin^(6)x cos^(5)x dx`
`=2int_(0)^(pi)sin^(6)xcos^(5)x dx [becausef(2pi-x)=f(x)]`
Let `f(x)=sin^(6)x cos^(5)x`
`f(pi-x)=sin^(6)(pi-x)*cos^(5)(pi-x)`
`=-sin^(6)x*cos^(5)x=-f(x)`
`therefore l =0`
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