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Topics in Integration

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Book cover Introduction to Numerical Analysis

Part of the book series: Texts in Applied Mathematics ((TAM,volume 12))

Abstract

Calculating the definite integral of a given real function f (x),

$$\int_a^b {f(x)dx,} $$

is a classic problem. For some simple integrands f (x), the indefinite integral

$$\int_a^x {f\left( x \right)} dx = F\left( x \right),F'\left( x \right) = f\left( x \right),$$

can be obtained in closed form as an algebraic expression in x and wellknown transcendental functions of x. Then

$$\int_a^b {f(x)dx = F(b) - F(a).} $$

See Gröbner and Hofreiter (1961) for a comprehensive collection of formulas describing such indefinite integrals and many important definite integrals.

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Würzburg, am Hubland, 8700, Würzburg, Germany

    J. Stoer

  2. Institut für Mathematik, Technische Universität, 8000, München, Germany

    R. Bulirsch

Authors
  1. J. Stoer
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  2. R. Bulirsch
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© 1993 Springer Science+Business Media New York

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Stoer, J., Bulirsch, R. (1993). Topics in Integration. In: Introduction to Numerical Analysis. Texts in Applied Mathematics, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2272-7_3

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  • DOI: https://doi.org/10.1007/978-1-4757-2272-7_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4757-2274-1

  • Online ISBN: 978-1-4757-2272-7

  • eBook Packages: Springer Book Archive

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