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Primitives of continuous functions via polynomials
University West, Department of Engineering Science, Division of Mathematics, Computer and Surveying Engineering.ORCID iD: 0000-0001-6594-7041
2022 (English)In: International Journal of Mathematical Education in Science and Technology, ISSN 0020-739X, E-ISSN 1464-5211, p. 1-5Article in journal (Refereed) Published
Abstract [en]

In standard books on calculus the existence of primitive functions of continuous functions is proved, in one way or another, using Riemann sums. In this note we present a completely different self-contained, however probably folkloristic, proof of this existence. Our proof combines, on the one hand, the so-called Stone Weierstrass theorem on uniform approximation of continuous functions on the unit interval by polynomials, and, on the other hand, a classical result from calculus on the existence of limits of differentiated sequences of functions. The sought for primitive is then constructed as the limit of primitives of the polynomials approximating the original function.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2022. p. 1-5
Keywords [en]
Primitive function; integral; polynomial
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:hv:diva-19316DOI: 10.1080/0020739X.2022.2129499ISI: 000867511300001Scopus ID: 2-s2.0-85139849437OAI: oai:DiVA.org:hv-19316DiVA, id: diva2:1707063
Available from: 2022-10-28 Created: 2022-10-28 Last updated: 2024-03-21Bibliographically approved

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Lundström, Patrik

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