The Generalized Method of Exhaustion
Classical Analysis and ODEs
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.math/0011078,
title = {The Generalized Method of Exhaustion},
author = {Anthony A. Ruffa},
journal= {arXiv preprint arXiv:math/0011078},
year = {2007}
}
Comments
7 pages, 3 figures provided separately as .gif files