Aplicações da integral definida na geometria espacial : volume de sólidos de revolução

Abstract

The main purpose of the research is to apply the concepts of the integral defined in Spatial Geometry, in order to obtain the volume of solids of revolution. The methodology used in this research is characterized as a bibliographic study, with a qualitative approach and exploratory nature, in which we will use books, dissertations and scientific articles, among others, as research instruments. To support our research, we rely on the studies of 18 authors, among them: Boyer (2010), Eves (2011), Mol (2013) regarding the history of Mathematics; Among the main foundations, Thomas Jr. (2002), Anton, Bivens and Davis (2007), Stewart (2008 and 2013), among others, stand out. We presented throughout the research that the applications of the definite integral go far beyond problems of areas under curves. Initially, a presentation of the historical aspects was made, highlighting some scientific personalities from ancient Greece that were of great relevance and that contributed significantly to the development of the Calculus. Then, we carry out an approach of integration techniques, specifically substitution integrals and parts. We present the concept of indefinite, defined integrals and the Fundamental Theorem of Calculus. Finally, we made an application of the integral defined in Spatial Geometry, in order to calculate the volume of solids of revolution from the concept of the defined integral.