The Generalized Method of Exhaustion

Details The Generalized Method of Exhaustion The Generalized Method of Exhaustion

2000-11-13

arxiv.org/abs/math/0011078v1

Mathematics

Classical Analysis and ODEs

7 pages, 3 figures provided separately as .gif files

Scientific paper

The method of exhaustion is generalized to a simple formula that can be used to integrate functions under very general conditions, provided that the integral exists. Both a geometric proof (following the usual procedure for the method of exhaustion) and an independent algebraic proof are provided. Applications provided as examples include use of the formula to generate new series for common functions as well as computing the group velocity distribution resulting from waves diffracted from an aperture.

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