Archimedes {RY212 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 2x2, bf 2 5x5 bt'2, assuming that h and b are positive. Then h use calculus to find the area of the region enclosed between the arch and the xaxis. Which of the following graphs represents the correct parabolic arch? {ii- A. E. ii? C. D. Q Y Q my a as XQ Q as l3. Which of the following is the correct integral to find the area? h 4h O A. A= h - X dx O B. A= 4h (h - y)dy 4h O C. A= h - dx