Teorema fundamental do cálculo: percepções, demonstração e algumas aplicações

Abstract

This research has as objectives the demonstration of the Fundamental Theorem of Calculus in a more clear and objective and the presentation of two application of this theorem. The justification for the choice of the theme is given by the fact that he establish the link between derivative and integral, one of the fundamental contents of a course in Differential and Integral Calculus, which provides us with abstract perceptions and study some of its applications. We started working through a literature search to present both a demonstration of TFC as adapted for two of its applications, being respectively the solution of a problem the Initial Value through the calculation of primitives and an application of Fhysics. Besides research, we realized that it would be important to investigate the level of understanding, specifically, students of 3rd and 7th period 2011.2 semester, our course in Mathematics, Campus IV, UFPB have to study this theorem. For this, we developed and applied a questionnaire composed of four essay questions and then conducted a brief review and discussion of it. The results obtained are discussed in our concluding remarks, where we understand that the knowledge base of students is very important so that they can learn new content, however to alleviate this deficiency, teachers can appropriate more resources that assist student learning among them, we highlight some of the issues that contextualization is also one of our general goals, because we believe that when certain content, especially the discipline of calculus are worked with applications to other sciences, students can realize their importance in other areas of knowledge.