Keynote Lecture: Integration in the Era of Computer Algebra

The use of computer algebra systems in Mathematics education could and should in uence the future curriculum how to teach integration. The traditional way only brie y touches the area problem, to switch very quickly to antidi erentiation. Graphical representations as well as symbolic and numeric capabilities of modern computer algebra systems like DERIVE enable enhanced teaching techniques: students can easily access graphical representations of area approximations, the integrals of many elementary functions can be determined by limits of Riemann sums, recurrence equations for de nite integrals can be automatically detected using partial integration. This method has the advantage that the students learn to judge the quality of area approximations better, that numerical integration methods easily can be studied, that the development is more on the historical lines, that the importance of the fundamental theorem can be better understood. Furthermore it is easy to study series representations, e.g., as a byproduct of integration techniques. Using DERIVE this leads to a new concept of how to teach integration which will be demonstrated by practical examples.