Improper Integrals: An Alternative Criterion

Katiuscia Teixeira (katiuscia.teixeira@ucf.edu), University of Central Florida. The topic Improper Integrals, often introduced in the second course of Calculus, is an important, though difficult concept for students to grasp, viz. [1–3]. In this article we discuss an alternative (geometric) criterion for an improper integral to diverge. While the criterion is indeed efficient and easy to apply, if one believes, like I do, that teaching Calculus is more than training students to manipulate formulas, then the opportunity to present and discuss the reasoning leading to such a result should be thought as more valuable than the criterion, per se. Let us start off with a classical example of divergent integral: ∫ 1