The Riemann Integral

  • Andrew Browder
Part of the Undergraduate Texts in Mathematics book series (UTM)


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.


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

Authors and Affiliations

  • Andrew Browder
    • 1
  1. 1.Mathematics DepartmentBrown UniversityProvidenceUSA

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