Teaching improper integrals with CAS

Abstract

When teaching how to compute improper integrals, the basic approach to compute such improper integrals is by definition. But, what happens if an antiderivative F for f or the above limits do not exist? the definition procedure cannot be used for these examples. In this talk we will show, as an application of advanced calculus subjects, how to compute this kind of improper integrals using a CAS. Laplace and Fourier transforms or Residue Theorem in Complex Analysis are some advance techniques which can be used for this matter. As an example of use, we will describe the file ImproperIntegrals.mth, developed in DERIVE 6, which deals with such computations. This utility file was first introduced at TIME 2014 Conference. Some CAS use different rules for computing integrations. For example RUBI system, a rule-based integrator developed by Albert Rich, is a very powerful system for computing integrals using rules. We will be able to develop new rules schemes for some improper integrals using ImproperIntegrals.mth. These new rules can extend the types of improper integrals that a CAS can compute. Finally, we will show some examples that we use with our students which can not be computed with the basic procedures implemented in CAS. Using the utility file ImproperIntegrals.mth, these examples will be easily solved.