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Improper Integrals

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Abstract

The need to extend the definition of the integral beyond the limits imposed in Chapter 4 becomes apparent quite quickly, sometimes even without noticing if we are not too careful. For instance, if we want to integrate f (x) = xp over [0,1] then we can write uncritically

$$ \int_0^1 {x^p dx = \left[ {\frac{{x^{p + 1} }} {{p + 1}}} \right]_0^1 = \frac{1} {{p + 1}}\left( {1^{p + 1} - 0^{p + 1} } \right) = \frac{1} {{p + 1}}.} $$

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  • DOI: 10.1007/978-0-85729-380-0_5
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© 2004 Springer-Verlag London

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Walker, P.L. (2004). Improper Integrals. In: Examples and Theorems in Analysis. Springer, London. https://doi.org/10.1007/978-0-85729-380-0_5

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  • DOI: https://doi.org/10.1007/978-0-85729-380-0_5

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-493-2

  • Online ISBN: 978-0-85729-380-0

  • eBook Packages: Springer Book Archive