Archimedes (287-212 B.C.), inventor, military engineer, physicist, and the greatest mathematician of classical times in the Western world, discovered that the area 4h under a parabolic arch is two-thirds the base times the height. Sketch the parabolic arch y = h - x", -b/2Exsb/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. Which of the following graphs represents the correct parabolic arch? O A. O B. c. OD. Ay Ay Ay XWhich of the following is the correct integral to find the area? h 47 O A. A= h - X dx O B. A= 4h (h - y)dy 4h C. A= h - 12 X dx Evaluate the integral. A=