Parametrization of Curves and Line Integrals with a CAS

Programming with Computer Algebra Systems (CAS) has become an important tool as a support in Computer lectures in Mathematics subjects aimed at Engineering degrees. In this paper, the authors present their teaching experience within the concept "Line Integration" with the help of two specific CAS: DERIVE and MAXIMA. When introducing the new concept of Line Integration to students, one of their most common problems is related to the concept of curve of integration. For this reason, in this paper, the authors introduce programming with CAS to ease the understanding of the classical curves. Throughout the execution of these programs, together with the graphical capabilities of CAS, the students can check easier the main properties involving the curves. Different alternatives to compute Line Integral are also introduced by means of programming with CAS. Examples of use of these programs are presented together with a discussion on the advantages, disadvantages and differences of both CAS. Finally, the conclusions obtained after using both CAS with our students and some related future work are stated.