\ \

The equation is .

Graph the equation :

Observe the graph:

The top half of the big loop on interval .

The bottom half of the small loop on interval . \ \

Area of the loop is .

By using symmetry area inside the larger loop and out side the smaller loop of . \ \

.

Apply formula : .

.

Area of the region that inside the larger loop and out side the smaller loop is

.

Area of the region that inside the larger loop and out side the smaller loop is

. \ \