The Riemann Integral

Tunc Geveci
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Tunc Geveci: San Diego State University, Department of Mathematics and Statistics

Chapter Chapter 4 in Advanced Calculus of a Single Variable, 2016, pp 169-259 from Springer

Abstract: Abstract In this chapter we define the Riemann integral in terms of upper and lower sums and arbitrary Riemann sums. We show that a wide class of functions and their combinations are Riemann integrable. We prove the Fundamental Theorem of Calculus, the substitution rule and integration by parts. We also discuss improper integrals.

Keywords: Riemann Integral; Substitution Rule; Improper Integral Diverges; Low Summer; Limit Comparison Test (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-27807-0_4

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DOI: 10.1007/978-3-319-27807-0_4

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