Let denote the area swept out by the curve as increases from to

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

Problem

Let

A(\theta)=\dfrac{1}{2}\displaystyle\int_{0}^{\theta}\bigl[2\bigl(1+\cos\varphi\bigr)\bigr]^2\,d\varphi

denote the area swept out by the curve

r=2\bigl(1+\cos\theta\bigr)

\varphi

increases from

0

\theta

, where

0\le\theta\le\pi

. For which value of

\theta

A(\theta)

maximized? (a)

\dfrac{3\pi}{4}

(b)

\dfrac{\pi}{2}

(c)

\pi

(d)

\dfrac{2\pi}{3}