The fundamental theorem of calculus within a geometric context based on Barrow's work

Abstract

The two main processes of calculus are integration and differentiation. These two processes are intimately related by being reciprocal to each other. This fact constitutes the fundamental theorem of calculus (FTC). In the present article, we explore this important theorem within a geometric context, based on Isaac Barrow's work from the seventeenth century. We argue that presenting and discussing the origins and development of the FTC is beneficial for first-year calculus courses.

Keywords:

• fundamental theorem
• calculus
• tangent
• quadrature

Acknowledgements

The authors would like to thank the reviewers for their valuable comments and suggestions to improve the quality of this article. Also, particular thanks to Kelly E. Matthews, Lecturer in Higher Education at the University of Queensland (Australia), for her insightful and thoughtful comments.