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The equation is .

Graph the equation :

Observe the graph:

The larger half loop on interval .

The small loop on interval .

Area of the loop is .

By using symmetry area inside the larger loop and enclosed 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

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