Let S be the solid generated when the region in the first quadrant bounded by the curves y=x and y=x2 is revolved about the x–axis.
(a) Determine the x–coordinates of the points where the two curves intersect in the first quadrant.
(b) Write a single definite integral that gives the volume of S.
(c) Evaluate the integral found in part (b) to obtain the exact volume of S.