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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.

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Revisiting the Notion of Integral: Calculus Versus Analysis

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  • 发表日期：

    2025年

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  • Ushangi Goginava,
  • Farrukh Mukhamedov,
  • Humberto Rafeiro

摘要

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.