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Evaluate : int (0)^(pi//2) sin^(3) x dx...

Evaluate : `int _(0)^(pi//2) sin^(3) x dx`

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`int _(0)^(pi//2) sin^(3) c dx`
`=int_(0)^(pi//2) (3 sin x -sin 3x)/(4) dx`
` =1/4 [-3 cos x +1/3 cos 3x] _(0)^(pi//2)`
`=1/4 [-3cos .(pi)/(2)+(1)/(3) cos. (3pi)/(2)]`
`-1/4 [-3cos 0 +(1)/(3) cos 0]`
`=0-1/4 (-3 +(1)/(3)) =(2)/(3).`
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