Let be the portion of the curve traced as varies from to

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

Problem

Let

C

be the portion of the curve

r = 3\cos\theta

traced as

\theta

varies from

0

\tfrac{\pi}{2}

. What is the exact area of the region enclosed by

C

and the initial ray

\theta=0

? (a)

\dfrac{9\pi}{16}

(b)

\dfrac{9\pi}{8}

(c)

\dfrac{9\pi}{4}

(d)

\dfrac{3\pi}{4}