A Truly Beautiful Theorem: Demonstrating the Magnificence of the Fundamental Theorem of Calculus

Abstract

SynopsisIn standard treatments of calculus, the Fundamental Theorem of Calculus is often presented as a computational method to evaluate definite integrals, with such powerful utility that one is tempted to overlook its beauty. To improve students' appreciation for the first part of the Fundamental Theorem of Calculus, we suggest a few classroom examples focusing on the accumulation function, to be introduced early and often throughout an introductory calculus course. These examples are small enough that they would not necessarily result in changes to a typical course schedule; yet we believe their contribution to student understanding can be significant. Furthermore, such examples might allow students to share more of the excitement that the pioneers of the subject surely experienced along the way.