Archimedes (287–212 B.C.), inventor, military engineer, physicist, and the greatest mathematician of classical times in the Western world, discovered that the area under a parabolic arch is two-thirds the base times the height. Sketch the parabolic arch y = h - (4h/b²)x², -b/2 ≤ x ≤ b/2, assuming that h and b are positive. Then use calculus to find the area of the region enclosed between the arch and the x-axis.