Approximations first: a closer look at applications of the definite integral^*

ABSTRACT

I propose that students pay more attention to the approximations that lead to integral formulas when they study applications of the definite integral. The goal is to focus students on the underlying concepts and the definition of the definite integral – and to steer them away from memorizing formulas. To address this goal, I have written some computer-based activities that guide students through the nuts and bolts of the approximations that eventually lead to integral formulas. I describe the activities and suggest a few changes as to how we might approach this material.

KEYWORDS:

• Calculus
• Riemann sum
• definite integral
• computer algebra system

AMS 2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 97A30
• 97D20
• 97D40
• 97I50

Acknowledgments

I would like to thank my colleague Derrick Hart for using some of the activities in his classes and providing me with valuable feedback, and I would like to thank my colleague John Koelzer for reviewing an early draft of this paper and for directing me to the books by Protter and Morrey, Stein, and Taylor. Also, I would like to thank the Don and Pat Morrison Foundation for its generous support of this project.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Don and Pat Morrison Foundation