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1993 | OriginalPaper | Buchkapitel

Topics in Integration

verfasst von : J. Stoer, R. Bulirsch

Erschienen in: Introduction to Numerical Analysis

Verlag: Springer New York

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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.

Metadaten
Titel
Topics in Integration
verfasst von
J. Stoer
R. Bulirsch
Copyright-Jahr
1993
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4757-2272-7_3