Visualization of the Riemann–Stieltjes Integral

Abstract

SummaryIt is desirable to have geometric interpretations of difficult mathematical concepts. In this paper, we present an intuitive geometric interpretation of the Riemann–Stieltjes integral. It can be summarized as follows: the Riemann–Stieltjes integral can be interpreted as an infinite sum of infinitesimally small non-rectangular integration strips. This interpretation is surprisingly similar to the geometric interpretation of the ordinary Riemann integral. It is therefore likely that students, when encountering the Riemann–Stieltjes integral for the first time, would find this new geometric framework a useful visualization tool.