Polar Coordinates: A Hard Area Problem
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This animation depicts a hard polar area problem.
(See notes below.)
Here, we see how the radius vector to a point moving along the curve r = 1 + cos θ
sweeps out the area of the region enclosed by one loop of the curve, but outside of the
region enclosed by the curve r = cos θ. Note that the region that lies inside
of the inner curve is swept out well before that of the region inside the outer curve
is completely swept out. This has consequences for the limits of integration needed
to solve the problem.