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If I(n)=int sin^(n)x dx, show that, I(...

If `I_(n)=int sin^(n)x dx`, show that,
`I_(n)=-(1)/(n) sin^(n-1)x cosx+(n-1)/(n).I_(n-2)`. Hence, evaluate,
`int sin^(6)x dx`.

Text Solution

Verified by Experts

The correct Answer is:
`-(1)/(6)cos xsin^(5)x-(5)/(24)cos x sin^(3)x-(5)/(16)sin x cosx+(5x)/(16)+c`
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