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The Evaluation of Definite Integrals as the Limits of Sums

Published online by Cambridge University Press:  03 November 2016

T. M. Flett
T. M. Flett*
Affiliation:
Department of Pure Mathematics, The University of Liverpool
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Extract

It is customary in an account of Riemann integration to give one or two examples of the evaluation of definite integrals directly from the definition of the integral in terms of Riemann (or Darboux) sums, but the method is used only to illustrate the definition, and is never fully exploited. The method is, however, capable of a more systematic treatment than one might at first expect, and in this note we show how it can be applied to some of the elementary functions of analysis.

Type
Research Article
Information
The Mathematical Gazette , Volume 46 , Issue 355 , February 1962 , pp. 6 - 13
Copyright
Copyright © Mathematical Association 1962

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References

page 10 note * The result of Theorem 3 can also be deduced from a general theorem on substitution in a Riemann integral.