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If I(m)=int (sin x+cos x)^(m)dx, then sh...

If `I_(m)=int (sin x+cos x)^(m)dx`, then show that `m l_(m)=(sin x+ cos x)^(m-1)*(sin x- cos x)+2(m-1) I_(m-2)`

A

`I_(4","2)=(1)/(6)(-sin^(3)x cos^(3)x+3I_(2","2))`

B

`I_(4","2)=(1)/(6)(sin^(3)x cos^(3)x+3I_(2","2))`

C

`I_(4","2)=(1)/(6)(sin^(3)x cos^(3)x-3I_(2","2))`

D

`I_(4","2)=(1)/(4)(-sin^(3)x cos^(3)x+2I_(2","2))`

Text Solution

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The correct Answer is:
A
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