Mathematical Analysis pp 98-122 | Cite as

# The Riemann Integral

Chapter

## Abstract

In this chapter we give an exposition of the definite integral of a real-valued function defined on a closed bounded interval. We assume familiarity with this concept from a previous study of calculus, but want to develop the theory in a more precise way than is typical for calculus courses, and also take a closer look at what kind of functions can be integrated. The integral to be defined and studied here is now widely known as the Riemann integral; in a later chapter we will study the more general Lebesgue integral.

## Keywords

Fundamental Theorem Cyclic Permutation Improper Integral Piecewise Linear Continuous Function Riemann Integral
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## Copyright information

© Springer Science+Business Media New York 1996