VI - RIEMANN INTEGRABLE FUNCTIONS

Abstract

This chapter discusses the Riemann Integrable Functions. The definition of the Riemann integral has a parallel that, with exactly the same notation, defines a certain area. Thus, the integral will exist only if the area does, and one may be used to find the other. The chapter describes the anti derivatives or differentiation of the integral. Corresponding to the mean value theorem for derivatives, there is a similar mean value theorem for integrals. It is the same sort of theorem in that it guarantees the existence of a point rather than describing a method of finding some point. Improper integrals explain that if the restrictions that the domain and the range of a function be finite are relaxed, the integral must be defined by a limiting process. This chapter also presents the convergence problem.