The curves and bound a region in the first quadrant ( )

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

Problem

The curves

r=2\sin\theta

and

r=2\cos\theta

bound a region in the first quadrant (

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

). Compute the exact area of this region. (a)

\dfrac{\pi}{2}-1

(b)

2

(c)

1

(d)

\dfrac{\pi}{2}