Symbolic and Graphical Investigations of Riemann Sums with a Computer Algebra System

ABSTRACT: This article explores the ways that a computer algebra system may be used in conjunction with plotting software to allow students to investigate the convergence properties of Riemann sums for functions of one or two variables in a way that is not possible with just numerical calculations. Explicit formulas for the Riemann sums suggest algebraic combinations that lead to the trapezoid and Simpson’s rules as a way to improve the rate of convergence