Evaluate the following integral:`int_0^(pi//2)x\ s in xcos^2x\ dx`

Explanation

Consider `{I}=int_{0}^{pi / 2} cos ^{2} {x} {dx} quad`.........(1)



`I=int_{0}^{pi / 2} cos ^{2}(frac{pi}{2}-x) d x quad(int_{0}^{a} f(x) d x=int_{0}^{a} f(a-x) d x)`




`I=int_{0}^{pi / 2} sin ^{2} x d x`


Adding 1 and 2 , we get,



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