Let be the cardioid given by

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

Problem

Let

C_1

be the cardioid given by

r=4\,(1+\cos\theta)

, and let

C_2

be the circle given by

r=4

. (1) Find all values of

\theta

between

0

and

2\pi

for which the two curves intersect. (2) Set up, but do not evaluate, a definite integral expression for the area that is inside

C_1

and outside

C_2

. (3) Evaluate the integral you set up in part (b) to obtain the exact area of the region common to

C_1

and outside

C_2

. Express your answer in terms of

\pi