Evaluate the following integral: `int_0^(pi//2)xsinx+cos^2x`

Explanation

Consider `I=int_{0}^{pi} x sin x cos ^{2} x d x.`




`I=int_{0}^{pi}(pi-x) sin (pi-x) cos ^{2}(pi-x) d x ldots ldots ldots ldots ldots .[int_{0}^{a} f(x) d x=int_{0}^{a} f(a-x) d x] `


`=int_{0}^{pi}(pi-x) sin x cos ^{2} x d x ldots ldots ldots ldots ldots .(2)
`



by Add eq (1) and (2), we get


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