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The Riemann Integral

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Book cover Lectures on the Hyperreals

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 188))

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Abstract

The definite integral ∫ba(x)dx represents the area under the graph of the function y = f(x) between x = a and x = b. The standard way to define this is to partition the interval [a, b] into a finite number of subintervals, approximate the desired area by sums of areas of rectangles based on these subintervals, and then take the limit as the number of subintervals is increased.

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© 1998 Springer-Verlag Berlin Heidelberg

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Goldblatt, R. (1998). The Riemann Integral. In: Lectures on the Hyperreals. Graduate Texts in Mathematics, vol 188. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0615-6_9

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  • DOI: https://doi.org/10.1007/978-1-4612-0615-6_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6841-3

  • Online ISBN: 978-1-4612-0615-6

  • eBook Packages: Springer Book Archive

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