Let $R$ be the region enclosed by the loop of the parametric curve $x=t^2,\;\;y=t^3-3t$.

(a) Find the area of $R$.

Area =

(b) If $R$ is rotated about the $x$-axis, find the volume of the resulting solid.

Volume =

(c) Find the coordinates of the centroid of $R$.

$(x, y) =$ (, )