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