A Note on Teaching the Riemann Integral

Abstract

Summary There are alternative definitions for the Riemann integral, many of which avoid some of the unpleasant computations that arise when using Riemann sums. In this version a simple distance function for step functions is used and the Riemann integral is defined and developed by employing exclusively “convergent” sequences of step functions. While only modestly different from the standard presentation it might have some extra intuitive appeal. This is a common device in advanced theories of integration and can be introduced at this elementary level.