A region in the plane is enclosed by the two polar curves and .

MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

A region

R

in the plane is enclosed by the two polar curves

r = 4 \cos \theta

and

r = 2 \cos \theta

. (a) Find all angles

\theta

where the two curves intersect. (b) Set up and evaluate an exact expression for the area of

R

. (c) Verify that your result is consistent with the fact that one curve is a dilation of the other about the pole.