The Generalized Method of Exhaustion

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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.
7 pages, 3 figures provided separately as .gif files

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Classical Analysis and ODEs, Mathematical Physics, 26B15;30B99;78A45

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http://salesiana.dossiersoluciones.com/handle/123456789/60324

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0011078
 http://arxiv.org/abs/math/0011078

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arXiv