The curve is defined by and for

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

Problem

The curve is defined by

x(t)=t^{2}

and

y(t)=\dfrac{t^{3}}{3}

for

0\le t\le 1

. Which of the following is the exact length of the curve on this interval? (a)

\dfrac{1}{2}\bigl(5\sqrt{5}-8\bigr)

(b)

\dfrac{1}{3}\bigl(5\sqrt{5}\bigr)

(c)

\dfrac{1}{3}\bigl(5\sqrt{5}-8\bigr)

(d)

\dfrac{1}{3}\bigl(5\sqrt{5}+8\bigr)