Skip to main content

Riemann Integration

Part of the Graduate Texts in Mathematics book series (GTM,volume 282)

Abstract

This brief chapter reviews Riemann integration. Riemann integration uses rectangles to approximate areas under graphs. This chapter begins by carefully presenting the definitions leading to the Riemann integral. The big result in the first section states that a continuous real-valued function on a closed bounded interval is Riemann integrable. The proof depends upon the theorem that continuous functions on closed bounded intervals are uniformly continuous.

Author information

Authors and Affiliations

Authors

Rights and permissions

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Reprints and Permissions

Copyright information

© 2020 Sheldon Axler

About this chapter

Verify currency and authenticity via CrossMark

Cite this chapter

Axler, S. (2020). Riemann Integration. In: Measure, Integration & Real Analysis. Graduate Texts in Mathematics, vol 282. Springer, Cham. https://doi.org/10.1007/978-3-030-33143-6_1

Download citation