मूल्यांकन कीजिएः
`int_(0)^(pi//2) cos^(3)xdx`

Explanation

`underset(0)overset(pi//2)int cos^(3)xdx`
`=underset(0)overset(pi//2)int ((cos 3x+3cosx)/(4))dx [therefore cos 3x=4cos^(3)x-3cosx]`
`=1/4 underset(0)overset(pi//2)int (cos 3x+3cos x)dx`
`=1/4 [(sin 3x)/(3)+ sin x]_(0)^(pi//2)`
`=1/4[{1/3sin((3pi)/(2))+3 sin((pi)/(2))}-{(sin 0)/(3)+3 sin 0}]`
`=1/4 [{1/3 xx (-1)+3}-(0+0)]`
`=1/4(-1/3+3)=1/4xx8/3=2/3`