A curve is defined parametrically by and for

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

Problem

A curve is defined parametrically by

x=t^{3}-t

and

y=t^{2}

for

0\le t\le 1

. Together with the

y

-axis, the curve encloses a region in the plane. What is the area of this region? (a)

\dfrac{8}{15}

(b)

\dfrac{4}{15}

(c)

\dfrac{2}{15}

(d)

\dfrac{2}{5}