The construction of the integral for the arc length of a curve based on van Heuraet and Fermat’s works

Abstract

We present the research outcomes of a project in Mathematics Education about the design and implementation of an instrument to learn the integral for the arc length of a function by using differential elements as the strategy for its construction. The research was done via a didactic intervention in a regular Integral Calculus course. The instrument was designed based on historical-epistemological analyses of the works of van Heuraet and Fermat. The main result of this research was that students achieve a more robust conceptualization of the integral for the arc length, supported by its construction with differential elements and its geometric foundation.

Disclosure statement

No potential conflict of interest was reported by the author(s).