A Lost Theorem: Definite Integrals in Asymptotic Setting

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dc.creatorCavalcante, Ray
dc.creatorTodorov, Todor D.
dc.date2008-04-19
dc.date.accessioned2026-07-07T09:33:41Z
dc.date.available2026-07-07T09:33:41Z
dc.descriptionWe present a simple yet rigorous theory of integration that is based on two axioms rather than on a construction involving Riemann sums. With several examples we demonstrate how to set up integrals in applications of calculus without using Riemann sums. In our axiomatic approach even the proof of the existence of the definite integral (which does use Riemann sums) becomes slightly more elegant than the conventional one. We also discuss an interesting connection between our approach and the history of calculus. The article is written for readers who teach calculus and its applications. It might be accessible to students under a teacher's supervision and suitable for senior projects on calculus, real analysis, or history of mathematics.
dc.identifierhttps://arxiv.org/abs/0804.3156
dc.identifierhttp://arxiv.org/abs/0804.3156
dc.identifierThe American Mathematical Monthly, Volume 115, Number 1, January 2008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159221
dc.subjectClassical Analysis and ODEs
dc.subjectGeneral Mathematics
dc.subject28A75, 28A99, 34E05, 26E35
dc.titleA Lost Theorem: Definite Integrals in Asymptotic Setting
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