The curve defined by and for forms a closed loop enclosing a finite region in the -plane

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

Problem

The curve defined by

x(t)=t^{2}-1

and

y(t)=t^{3}-3t

for

-\sqrt{3}\le t\le \sqrt{3}

forms a closed loop enclosing a finite region in the

xy

-plane. What is the area of this region? (a)

\dfrac{24}{5}

(b)

\dfrac{24}{5}\sqrt{3}

(c)

\dfrac{12}{5}\sqrt{3}

(d)

\dfrac{48}{5}\sqrt{3}