Find a definite integral expression that represents the area of the region inside one loop of the lemniscate $r ^ { 2 } = \sin 2 \theta$ Then find the exact value of the integral.

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The Answer of Find a definite integral expression that represents the area of the region inside one loop of the lemniscate $r ^ { 2 } = \sin 2 \theta$ Then find the exact value of the integral.

Find a Definite Integral Expression That Represents the Area of the Region