The curve is , .

Find the area of the region under the curve using graphing utility.

Graphically the area of the region under the curve is . 

Determine the exact area by integrating the curve under the given limits.

Area is .

Double angle identity: .

Rewrite the integral as ..

Consider .

Apply derivative on each side.

.

Change in integral limits:

Lower limit: If  then .

Upper limit: If  then .

Substitute ,  and change of limits in .

.

Area is .

Area is .