Elements for a didactic argument from the historical study of Newton's Fundamental Theorem of Calculus

Abstract

This paper, which follows the historiographic approach and is framed within the author's doctoral thesis research, it evidences an argument employed by Isaac Newton in his studies that culminated in a version of what is currently recognized as the Fundamental Theorem of Calculus (FTC). From this perspective, the CFT will be analyzed in four different periods, 1665, 1666, 1669, and 1704 of Newton's work. The characteristics of this argument can be converted into a structure for alternative presentation in the TFC teaching to university students since heuristics plays an important role in problem-solving. Then, the pretension that it becomes another resource for the teaching of TFC would be based on retaking it as the relation between the problem of the areas and the inverse problem of the tangents, beyond the usual one, i.e., the inverse relationship between the derivative and the integral.