Cálculo de áreas por meio das integrais definidas e impróprias

Abstract

The present work investigates the calculation of the area of flat figures with curvilinear contours using defined and improper integrals. We present historical aspects of the Integral and Differential Calculus and we also illustrate, algebraically and geometrically, the integrals as Riemann sums. We highlight the Fundamental Theorem of Calculus and its proof, as well as the main properties of definite and improper integrals and, finally, the divergence of certain improper integrals just using limits. We conclude that this work is potentially useful as didactic material in undergraduate courses.