Consider the region S enclosed by the parabola y2=4x and the line y=2x−4.
(a) Rewrite each curve in the form x=f(y).
(b) Find the exact y-coordinates of all points where the two curves intersect.
(c) Set up—but do not evaluate—a single definite integral with respect to y whose value equals the area of S. Clearly indicate the integrand and the limits of integration.
(d) Evaluate the integral from part (c) to obtain the exact area of S.