Date of Award


Document Type


Degree Name

Master of Science

Degree Discipline



The primary objective of this paper is a close examination of the differences in the class of functions f and g when f is Integrable with respect to g according to the definition of the integral based on the use of upper and lower sums as compared to the definition of the integral based on the trapezodial sum approach. The differences in the proofs of certain theorems relative to the properties and existence of the Integral will also be examined.

In order to clearly distinguish between these approaches to the integral, the writer considers only one method of taking limits of the defining sums, namely the refining of partitions. Clearly, the limit of these sums under the requirement of the norm of the partitioning having limit zero introduces another difference in the possible existence of the integral and is not considered in this paper.

Committee Chair/Advisor

Ralph Whitmore

Committee Member

A. D. Stewart


Prairie View Agricultural and Mechanical College


© 2021 Prairie View A & M University

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Date of Digitization


Contributing Institution

John B Coleman Library

City of Publication

Prairie View




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