On the interval

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

Problem

On the interval

0\le\theta\le\dfrac{\pi}{2}

, consider the curves

r=2

and

r=2+a\sin\theta

where

0\le a\le 2

. Determine the value of

a

that maximizes the area of the region lying between the two curves on this interval.