Let for . Calculate the exact length of the…

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

Problem

Let

\mathbf r(t)=\langle t^{2},\tfrac13 t^{3}\rangle

for

0\le t\le2

. Calculate the exact length of the curve. (a)

\displaystyle \frac{16\sqrt{2}-4}{3}

(b)

\displaystyle \frac{8\sqrt{2}-8}{3}

(c)

\displaystyle \frac{16\sqrt{2}-8}{3}

(d)

\displaystyle \frac{16\sqrt{2}-8}{6}