Question

`int_0^{pi/2} cos^2x  dx` = ______ 

Options

• `pi/4`

• `pi/3`

• `pi/2`

• π

Answer 1

`int_0^{pi/2} cos^2x  dx` = `underline(pi/4)`

Explanation:

`int_0^{pi/2} cos^2x  dx = int_0^{pi/2} ((1 + cos2x)/2) dx`

= `1/2[int_0^{pi/2} 1 dx + int_0^{pi/2} cos 2x dx]`

= `1/2[[x]_0^{pi/2} + [(sin2x)/2]_0^{pi/2}]`

= `1/2[(pi/2 - 0) + (1/2 sinpi - 0)] = pi/4`