Revisiting the Notion of Integral: Calculus Versus Analysis

Ushangi Goginava (), Farrukh Mukhamedov () and Humberto Rafeiro ()
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Ushangi Goginava: Mathematical Sciences - (COS), United Arab Emirates University
Farrukh Mukhamedov: Mathematical Sciences - (COS), United Arab Emirates University
Humberto Rafeiro: Mathematical Sciences - (COS), United Arab Emirates University

A chapter in Handbook of Visual, Experimental and Computational Mathematics, 2026, pp 573-588 from Springer

Abstract: Abstract In honor of the bicentennial of Cauchy’s groundbreaking work on integration, we present a small survey of different integrals, shedding light on the underlying connections and showing the equivalence between these seemingly different integrals. Of particular interest, especially in the context of teaching calculus, is the equivalence between the Riemann integral and the equidistributed integral, which nowadays is the standard definition of integral in calculus textbooks.

Keywords: Cauchy integral; Riemann integral; Darboux integral; Newton integral; Equidistributed integral (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16368-4_52

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DOI: 10.1007/978-3-032-16368-4_52

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