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/b^2)x^2​, −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.

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