`int_0^(pi/2) cos^2(theta) d theta` Evaluate the integral

`int_0^(pi/2)cos^2(theta)d(theta)`

Use the identity: `cos^2x=(1+cos(2x))/2`

`intcos^2(theta)d(theta)=int(1+cos(2theta))/2d theta`

`=1/2int(1+cos(2theta))d theta`

`=1/2(int1d theta+intcos(2theta)d theta)`

`=1/2(theta+sin(2theta)/2)`

add a constant C to the solution,

`=1/2(theta+sin(2theta)/2)+C`

`int_0^(pi/2)cos^2(theta)d theta=[1/2(theta+sin(2theta)/2)]_0^(pi/2)`

`=[1/2(pi/2+sin(2*pi/2)/2)]-[1/2(0+sin(0)/2)]`

`=[1/2(pi/2+0/2)]-[1/2(0)]`

`=pi/4`