Question

Solve ${\int }_0^{\frac{\pi }{2}}{\cos }^{2}xdx$

Answer 1

${\int }_0^{\pi /2}{\cos }^{2}xdx=\frac{1}{2}{\int }_0^{\pi /2}(1+\cos 2x)dx=\frac{1}{2}[x+\frac{\sin 2x}{2}{]}_0^{\pi /2}=\frac{\pi }{4}$