The integral is .

Rewrite the integral as .

Consider .

Substitute .

Apply derivative on each side with respect to .

Substiute the corresponding values in the integral.

Apply double angle formula : .

.

If  then 

.

(a) Apply integration limits.

.

(b)

Apply trigonometric limits in equation .

.

If  then .

If  then .

.

(a) By the integration limits :.

(b) By the limits obtained by the trigonometric substitution :.