Evaluate the following definite integral: `int_0^(pi//2)x^2sinx\ dx`

Explanation

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

By using integration by parts, we get
`

I=.x^{2}(-cos x)|_{0} ^{frac{pi}{2}}-int_{0}^{frac{pi}{2}} 2 x(-cos x) d x `
`
Rightarrow I=(0-0)+2 int_{0}^{frac{pi}{2}} x cos x d x ldots ldots ldots(cos frac{pi}{2}=0) `


Again using integration by parts, we have
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