Let be the region that is inside the polar curve and outside the polar curve .

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

Problem

Let

R

be the region that is inside the polar curve

r=4\cos\theta

and outside the polar curve

r=2

. (a) Solve for all values of

\theta

with

0\le\theta\le 2\pi

at which the two curves intersect. (b) Set up, but do not yet evaluate, a single integral that represents the area of

R

. (c) Evaluate the integral in part (b) to obtain the exact area of

R

. Express your answer in terms of

\pi