Introducción a la integración en términos finitos

Abstract

The Mathematics program at ESPOCH addresses the topic of integration within the course Mathematical Analysis. However, a lack of focus on integration in finite terms is evidenced, as this topic is not covered in the course curriculum. Therefore, this research aims to develop a document intended to serve as a study guide for students of Mathematical Analysis, focusing specifically on finite integration. The approach of this research work is documentary in nature, with a qualitative orientation justified by the literature review related to the topic. A detailed study was conducted based on the selection of the most outstanding bibliographic sources, exploring theorems and lemmas that determine the existence of the elementary antiderivative of an elementary function. Additionally, numerical methods to calculate the integral of a given function when feasible, were addressed. At the conclusion of this research, a document titled Introduction to Finite Term Integration was produced, which is expected to provide a deeper understanding for students of the Mathematics program. This document will allow them to easily determine whether an elementary function has an elementary antiderivative. As a suggested extension to the present research, it is proposed to carry out a study on the existence of antiderivatives of functions in the realm of complex numbers or in higher-dimensional spaces. Furthermore, the formulation of more efficient methods for calculating integrals is also recommended.