of antiquity Several calculus problems were solved by
Chapter 5, Problem 59(choose chapter or problem)
of antiquity Several calculus problems were solved by Greek mathematicians long before the discovery of calculus. The following problems were solved by Archimedes using methods that predated calculus by 2000 years. a. Show that the area of a segment of a parabola is 43 that of its inscribed triangle of greatest area. In other words, the area bounded by the parabola y = a2 - x2 and the x-axis is 43 the area of the triangle with vertices 1{a, 02 and 10, a22. Assume that a 7 0 but is unspecified. b. Show that the area bounded by the parabola y = a2 - x2 and the x-axis is 23 the area of the rectangle with vertices 1{a, 02 and 1{a, a22. Assume that a 7 0 but is unspecified.
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