The integral defined as the area under a curve in a computational environment

Abstract

This paper is a summary of the doctoral thesis, “Teaching-learning process of the definite integral as an area under a curve in the course of calculus for engineering students in the Multidisciplinary Regional Faculty of Estelí. (FAREM – Estelí) . The scientific field within which this study is located in the Didactics of Mathematics, in the research area of educational quality. This research aimed to develop the conceptual field of calculus and its teaching-learning. Two main aspects are considered: first, its cognitive scope through which curricular material was prepared with the objective of introducing a primary study of the calculation of primitives, the concept of definite integral as an area under a curve from a graphical and numerical perspective. The second was an affective aspect consisting of analyzing the attitudes of the students about confidence, security, motivation, commitment, and use of the computer in the mathematical work. The selected students ware taking the differential and Integral calculus course in the discipline of Environmental Engineering and Renewable Energies Engineering. It is concluded that the elaboration of a compendium is a useful tool in the teaching and learning of calculus. Concerning the attitudes, it was found that the use of the computer gives confidence and security. In addition to being motivating, it engages the student in the realization of mathematical activities.