AP Calculus BC glossary
Polar area
The area enclosed by a polar curve is the integral of one half r squared with respect to theta. The region is built from circular sectors rather than rectangles, which is where the one half and the square come from.
Choosing the limits is the hard part. They must be the angles that sweep the region exactly once, so a curve that retraces itself needs a restricted interval rather than a full turn.
The mistake
Forgetting to square r, or dropping the one half. Both come from the sector area formula, not from the Cartesian area integral.
Appears in: Unit 9: Parametric, Polar, and Vector (BC)