Evaluate the following integrals: `int_0^picosx|cosx|dx`

Explanation

`int_{0}^{pi / 2} cos ^{2} x d x-int_{pi / 2}^{pi} cos ^{2} x d x`
`
=cos ^{2} x=frac{1+cos 2 x}{2}`
`
=int_{0}^{frac{pi}{2}} frac{1+cos 2 x}{2} d x-int_{frac{pi}{2}}^{pi} frac{1+cos 2 x}{2} d x`
`
=frac{1}{2}{frac{1+cos 2 x}{2}}_{0}^{frac{pi}{2}}-frac{1}{2}{x+frac{sin 2 x}{2}}_{frac{pi}{2}}^{pi}`
`
=frac{pi}{4}-frac{pi}{4}`
`
=0`