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Evaluate : int0^(pi/2)x^2sinxdx...

Evaluate : `int_0^(pi/2)x^2sinxdx`

Text Solution

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`int_0^(pi/2)x^2sinxdx`
`=-x^2cosx+int_0^(pi)1/2 2xcosxdx`
`=-x^2cosx+2{xsinx-int_0^(pi)/2sinxdx}`
`=(-x^2cosx+2xsinx+2cosx)_0^(pi)/2`
`=2((pi)/2)-2`
`=pi-2`
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