Mathematics

Problem

A particle moves in the plane with parametric equations

x(t)=t^{2}

and

y(t)=t^{3}

for

0\le t\le2

. Which definite integral equals the total distance traveled by the particle on this interval? a)

\displaystyle\int_{0}^{2}\sqrt{(2t)^{2}+(3t^{2})^{2}}\,dt

\displaystyle\int_{0}^{2}\sqrt{1+\left(\dfrac{dy}{dx}\right)^{2}}\,dt

\displaystyle\int_{0}^{2}\bigl((2t)^{2}+(3t^{2})^{2}\bigr)\,dt

\displaystyle\int_{0}^{2}\sqrt{(2t)^{2}+(3t)^{2}}\,dt