The Existence of The Definite Integral: Students’ Understanding

Abstract

The definite integral is a part of a compulsory subject, Integral Calculus, for mathematics education students. As pre-service mathematics teachers, students’ understanding of the definite integral concepts is crucial to note. This article presents the result of the investigation students’ understanding of the definition of the definite integral and its existence. The study reported in this paper was done through qualitative research. A questionnaire about the definition of the definite integral and the existence of the definite integral of a defined function on a closed interval was given to 163 students who took Integral Calculus course. Then, 4 of them were selected to interview in depth. The students’ responses indicated the diversity of the conceptual understanding of the existence of the definite integral. Various students’ understanding of the definition of the definite integral that leads to students’ understanding of the existence of the definite integral is presented as well.