Teorema fundamental do cálculo: um grande desenvolvimento para o cálculo integral

Abstract

This work presents an investigation into one of the main discoveries in the history of mathematics - The Fundamental Theorem of Calculus (TFC). Carried out and published in the 17th century, it enabled significant advances in mathematics and, consequently, in other areas of exact sciences, since its main characteristic is to connect Differential Calculus and Integral Calculus. By contemplating in a clear, objective and reliable way the main factors surrounding the development of this theorem, it can be understood in a comprehensive manner, as well as other mathematical tools. In order to justify its importance for mathematics, especially for Integral Calculus, it is essential to know relevant historical facts such as the creation of mathematical symbolisms, the emergence of infinitesimal numbers, as well as the development of Analytical Geometry, for example. Allied to this, based on prestigious works within the academic community, explain it explicitly, apply it in problem situations involving integrals and derivatives and then compare these procedures, as well as the results obtained with certain methods. traditional methods used before this discovery help us understand why the Fundamental Theorem of Calculus stands out within Integral Calculus.