Region lies in the first quadrant and is bounded by the polar curve

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Region

S

lies in the first quadrant and is bounded by the polar curve

r = 4\cos\theta

, the

x

-axis, and the

y

-axis. Computing its area in polar form or by the rectangular description

0 \le x \le 4

and

0 \le y \le \sqrt{4x - x^{2}}

yields the same value. Which of the following is that value? (a)

\dfrac{8\pi}{3}

(b)

4\pi

(c)

2\pi

(d)

\pi