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int(0)^(pi//4) cos^(2) x dx...

`int_(0)^(pi//4) cos^(2) x dx`

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`int_(0)^(pi//2)cos^(2)x dx =int_(0)^(pi//2)((cos2x +1)/(2))dx`
`=(1)/(2) int_(0)^(pi//2)cos 2x dx +(1)/(2)int_(0)^(pi//2)1dx`
`=(1)/(2)[(sin 2x)/(2)]_(0)^(pi//2)+(1)/(2)[x]_(0)^(pi//2)`
`=(1)/(2)[((sinpi)/(2)-(sin 0)/(2))+((pi)/(2)-0)]=(pi)/(4)`
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