The value of `int_(-pi)^pisin^3xcos^2x\ dx\ ` is `(pi^4)/2` b. `(pi^4)/4` c. `0` d. none of these

Explanation

`int_{-pi}^{pi} sin ^{3} x cos ^{2} x d x `

`=int_{-pi}^{pi} sin x(1-cos ^{2} x) cos ^{2} x d x`


Let `cos x=t, then -sin x d x=d t,`

When `x=-pi, t=-1, x=pi, t=-1`

Therefore the integral becomes


`int_{-1}^{-1}-(1-t^{2}) t^{2} d t `

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