A proposal involving the area calculation of under curves using GeoGebra for High School

Abstract

This paper proposes an approach for teaching the calculation of areas under curves in high school, without directly resorting to Riemann's integration theory. The proposal uses geometric approximation methods, such as the use of rectangles and trapezoids with the support of GeoGebra software to obtain estimates of the area under curves of the form y = f(x), for x in an interval [a,b]. The present proposal introduces the functionsf(x) = x, f(x) = x² and f(x) = x³ defined on [a,b], whose area calculation is done by approximation, by dividing the interval into n subintervals, combining practical activities of manual calculation with GeoGebra and providing a comparative analysis between the approximation methods. As a result, it is expected that, through this proposal, students will be encouraged to reflect on the accuracy of estimates, seeing through the approach that the greater the number of divisions into rectangles and trapezoids of the area to be calculated, the closer the measurement of the area estimated through the technological tools will be, opening the way for the introduction of the study of Riemann sums and integrals in advanced stages of the training process.