Solved: Archimedes showed that the area of a parabolic arch is equal to the product of
Chapter 0, Problem 7(choose chapter or problem)
Archimedes showed that the area of a parabolic arch is equal to \(\frac{2}{3}\) the product of the base and the height (see figure).
(a) Graph the parabolic arch bounded by \(y=9-x^{2}\) and the x-axis. Use an appropriate integral to find the area A.
(b) Find the base and height of the arch and verify Archimedes' formula.
(c) Prove Archimedes' formula for a general parabola.
Text Transcription:
2/3
y=9-x^2
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