`int_0^(pi//2)xsinx\ dx` is equal to `pi//2` b. `pi//4` c. `pi` d. `1`

Explanation

`1`

We have,


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

`=[-x cos x]_{0}^{frac{pi}{2}}-int_{0}^{frac{pi}{2}} 1(-cos x) d x `

`=[-x cos x]_{0}^{frac{pi}{2}}+int_{0}^{frac{pi}{2}} cos x d x `

`=-[x cos x]_{0}^{frac{pi}{2}}+[sin x]_{0}^{frac{pi}{2}} `

`=-[0-0]+[1-0] `

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