Function identity and the fundamental theorem of calculus

Abstract

By analyzing the responses of 100 introductory calculus students to two questions, this study addresses how students understand the fundamental theorem of calculus as it relates to function identity. One question involves students’ understandings of the fundamental theorem of calculus, and the other involves their concept definitions of function sameness. This analysis aims to better understand students’ concept images of function sameness, both in the context of the fundamental theorem of calculus and in general.