Teaching mathematical integration: human computational skills versus computer algebra

摘要

Despite the ready availability of computer algebra packages, from a pedagogical point of view, the authors still feel that integration should be taught extensively the classical way, by means of carefully selected examples which combine as many fundamental techniques as possible for their evaluation. Furthermore, whenever possible, these examples should be specifically selected from those which a Computer Algebra System (CAS) either cannot solve precisely to provide an exact answer in analytical or transcendental form, or which a CAS cannot solve altogether. This approach ensures that students gain a proper understanding of the topic and, perhaps even more important, the fact that the students can evaluate precisely in closed form integrals which the computer cannot, stimulates and motivates them further to study these techniques. This note illustrates the above claims by means of both an indefinite integral and the associated improper integral which is offered to students as the 'integral of the year'.