International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 6, Pages 345-351
doi:10.1155/S0161171202011638
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 Anthony A. Ruffa. 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.
Abstract
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.