The Definite Integral

Abstract

In Section 5.2 we investigated the limit of a finite sum for a function defined over a closed interval [a, b] using n subintervals of equal width (or length), In this section we consider the limit of more general Riemann sums as the norm of the partitions of [a, b] approaches zero. For general Riemann sums the subintervals of the partitions need not have equal widths. The limiting process then leads to the definition of the definite integral of a function over a closed interval [a, b]. Limits of Riemann Sums The definition of the definite integral is based on the idea that for certain functions, as the norm of the partitions of [a, b] approaches zero, the values of the corresponding Riemann sb-ad>n.