When we need to find the area bounded by a single loop of the polar curve, we’ll use the same formula we used to find area inside the polar curve in general. We’ll integrate over the interval that defines the loop.
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The area inside a polar curve is given by a formula for A, where [alpha,beta] is the interval over which we’re integrating, and where r is the equation of the polar curve. Plugging everything into the formula will let us calculate the area bounded by the polar curve.
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