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International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 6, Pages 345-351

The generalized method of exhaustion

Naval Undersea Warfare Center Division, 1176 Howell Street, Newport 02841-1708, RI, USA

Received 22 January 2001; Revised 15 June 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The method of exhaustion is generalized to a simple integration formula that is valid for the Riemann integrable functions. Both a geometric approach (following the usual procedure for the method of exhaustion) and an independent algebraic generalization approach 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.