Integrais múltiplas em coordenadas polares: fatos para utilização do jacobiano

Abstract

When studying calculus, in what circumscribes the aspects learned at the level of higher education, the integrals are constructed and solved by several techniques disseminated in the mathematical literature. A specific study on polar coordinates, in terms of construction, definition, graphs and applications, was opportunized in this work, where a research was developed in the field of the Scholarship Program (PIBIC), where the application in the region defined in coordinates polar and the use of double integrals, necessitates the change of variable to solve problems, hence we propose research on indications that qualify the use of the Jacobian. The problems that involve multiple integrals in polar coordinates, surround as main axis of approach the changes of variables, besides which, they also understand the treatment of the question of investigating, which indications point the assembly of the Jacobian for the purpose of change of variables. In order to qualify the insertion of the change of variables, to perceive graphical or algebraic indicatives that enable a specific or non-Jacobian treatment to solve the integrals under study. This work circumscribes an activity of bibliographic and procedural research for a construction-selection of concepts, based on the discussions of Anton H; Bivens I.C; Davis S. L (2010), Gonçalves B. M; Flemming D. M (2013), and Wrede R.C; Spiegel M. S (2004), and to base with teaching methods and bases for the methodology, used in this work was referenced Quivy and Campenhoudt (1995). Therefore, it was possible to conclude that, by relating aspects that integrate the themes studied in historical and overlapping contexts, it was also possible to find out how the authors approach the themes. With everything, it was identified in the work materials, mathematical modeling, relating the logical reasoning of meaningful learning and the Jacobian applicability process.