Fundamental Theorem of Calculus: an epistemological analysis - Patrícia Benevides de Oliveira; Franck Gilbert René Bellemain (Amazônia, 2022)
In this article, we present an epistemological analysis based on a literature review about the development of the Fundamental Theorem of Calculus over time, through problem solving by mathematicians since Antiquity. We conclude that the relationship between the accumulation of a quantity (determination of area) and the rate of change of its accumulation (determination of the tangent), which culminated in the fundamental theorem, is one of the main milestones in the development of Calculus. These two classes of problems, known today as integration and derivation, were conceived separately, each one with techniques limited to the type of problem addressed, which ended up influencing the teaching of Calculus as we know it today.