Using properties evaluate the following definite integrals `int_0^(pi/2) cos^2x dx`

Explanation

Let I = `int_0^(pi/2) cos^2 x dx` ____(a)
Then I = `int_0^(pi/2) cos^2 (pi/2-x)dx`
=`int_0^(pi/2) sin^2 x dx` ____(b)
(a)+(b)
`gt2I = int_0^(pi/2) (cos^2x+sin^2x)dx`
=`int_0^(pi/2) dx = [x]_0^(pi/2) = pi/2-0 = pi/2`
Thus, I = `pi/4`