Antiderivatives Exist without Integration

2012/12/05 by Charles A. Coppin, Charles Coppin, Coppin, Charles
Computer Science · Mathematics · #FOS: Mathematics #Functional Equations Stability Results #History and Overview (math.HO) #Meromorphic and Entire Functions #Numerical Methods and Algorithms #math.HO

paper · pdf · doi:10.48550/arxiv.1212.1412

Three pages

arxiv created 2012/12/05 · openalex publication_date 2012/12/05 · arxiv updated 2012/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a proof that any continuous function with domain including a closed interval yields an antiderivative of that function on that interval. This is done without the need of any integration comparable to that of Riemann, Cauchy, or Darboux. The proof is based on one given by Lebesgue in 1905.

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