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Constructive Integration

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Abstract

In a first course in calculus, the integral is usually introduced as an ‘antiderivative’, i.e. given f, we look for a function F such that F′ = f. This works well enough when f is given by a simple formula, but the class of functions for which it succeeds is difficult to identify — who knows whether there is a function F with F′ (x) = sin \( x/\sqrt {1 - x^7 } \)

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  • DOI: 10.1007/978-0-85729-380-0_4
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© 2004 Springer-Verlag London

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Walker, P.L. (2004). Constructive Integration. In: Examples and Theorems in Analysis. Springer, London. https://doi.org/10.1007/978-0-85729-380-0_4

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  • DOI: https://doi.org/10.1007/978-0-85729-380-0_4

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-493-2

  • Online ISBN: 978-0-85729-380-0

  • eBook Packages: Springer Book Archive