A notion of primitive that fits the Riemann integral

Winston Alarcon-Athens

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arXiv · 1112.0957

A notion of primitive that fits the Riemann integral

Winston Alarcon-Athens

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Abstract

We present a notion of primitive which corresponds exactly with the Riemann integral. We obtain a characterization of the integrability in the sense of Riemann which produces a Fundamental Theorem of Calculus without special assumptions. We prove a lemma which generalizes the theorem on functions with zero derivative in an interval. We apply these concepts, sketching a simplified alternative presentation of the Riemann integral in R.

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Winston Alarcon-Athens. 2011-12-01. A notion of primitive that fits the Riemann integral. https://arxiv.org/abs/1112.0957

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