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

The generalized method of exhaustion

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.