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Topics in Integration

  • J. Stoer
  • R. Bulirsch
Part of the Texts in Applied Mathematics book series (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.

Keywords

Asymptotic Expansion Orthogonal Polynomial Step Length Extrapolation Method Hermite Interpolation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References for Chapter 3

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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • J. Stoer
    • 1
  • R. Bulirsch
    • 2
  1. 1.Institut für Angewandte MathematikUniversität WürzburgWürzburgGermany
  2. 2.Institut für MathematikTechnische UniversitätMünchenGermany

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