The curve given by and for forms a closed loop

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

Problem

The curve given by

x(t)=2\sin t

and

y(t)=2\sin t\cos t

for

0\le t\le\pi

forms a closed loop. Compute the exact area enclosed by this loop.