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

Explanation

`I=int_{0}^{pi / 2} cos ^{2} x d x`
`
=int_{0}^{pi / 2} frac{1+cos 2 {x}}{2} {dx} ldots ldots ldots ldots . . . ldots(cos 2 {x}=2 cos ^{2} {x}-1) `
`
=frac{1}{2}[x+frac{sin 2 x}{2}]_{0}^{pi / 2}`
`
=frac{1}{2}[(frac{pi}{2}+frac{sin pi}{2})-(0+frac{sin 0}{2})]`
`
=frac{pi}{4}`
`