Chapter 9.2, Problem 32E

(a)

To determine

The area of the region enclosed by the loop of the curve drawn using the parametric equations of $x=t^2$ and $y=t^3-3t$.

(b)

To determine

The volume of resulting solid if the region enclosed by the loop of the curve is rotated about the $x$ axis for the parametric equations of ellipse $x=t^2$ and $y=t^3-3t$.

(c)

To determine

The coordinates of the centroid of $\Re$ region enclosed by the loop of the curve, drawn using the parametric equations of $x=t^2$ and $y=t^3-3t$.