Contribution of the probability to the analytical calculation of defined integrals

Abstract

In view of the importance of integrals in numerous areas, finding methods that provide exact values of defined integrals is extremely important. In this article, an alternative way of solving defined integrals, using the Normal and Chi-square distributions will be presented, showing the possible contribution of Probability to the teaching and learning of Integral Calculus. The proposed method, in addition to being an alternative procedure for solving defined integrals with the same precision as the techniques found in Integral Calculation books, offers the advantage that the exact solution of defined integrals that cannot be resolved by the usual techniques can be determined. For the presentation of the proposed method, theoretical support will be provided for a better understanding of the reader. In this sense, the probability distribution functions, their properties and the Fundamental Theorem of Calculus will be emphasized. Subsequently, two integrals defined that are not resolvable by the usual techniques will be calculated using the Normal and Chi-square distributions, following to generalize the functions that can be integrated using these distributions.