(a) Use R to plot the curve of the following cubic function

y=1/3 x^3

for-2 ≤ ≤ 2.

(b) Find the curvature function of this curve following the approach of x = |dT/ds = T' (t)/r' (t).

(c) Find the length of this parabola for -1 ≤ ≤ 1. Set up an integral for the length and evaluate the integral by R using integrate (). Hint: Let a = t

and y=t³.