The motion of a particle in the plane for 0≤t≤4 seconds is described by the parametric equations x(t)=t2+1,y(t)=31t3. At t=0 the particle is at (1,0).
(a) Write a definite integral that gives the distance traveled by the particle from t=0 to t=4.
(b) Using four subintervals of equal length, approximate the integral from part (a) with the Trapezoidal Rule. Show your set-up and final numerical result.
(c) Interpret the value obtained in part (b) in the context of the particle’s motion, including appropriate units.