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intsin^(3)xcos^(3)xdx=?...

`intsin^(3)xcos^(3)xdx=?`

A

`-(1)/(4)cos^(4)x+(1)/(6)cos^(6)x+C`

B

`(1)/(4)sin^(4)x-(1)/(6)sin^(6)x+C`

C

`(1)/(4)sin^(4)x+(1)/(6)cos^(6)x+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`I=intsin^(3)cos^(2)xcosxdx=intsin^(3)x(1-sin^(2)x)cosxdx`.
`=intt^(3)(1-t^(2))dt`, where sin x=t
`=int(t^(3)-t^(5))dt=(t^(4))/(4)-(t^(6))/(6)+C=(1)/(4)sin^(4)x-(1)/(6)sin^(6)x+C`.
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