Is close enough good enough? Reflections on the use of technology in teaching calculus

Abstract

In this note, we introduce an interesting example that uses the monotonicity of the definite integral to obtain a good approximation of a particular definite integral. The second objective of this note is to discuss some aspects of the place of technology in teaching calculus topics.

Keywords:

• definite integral
• approximation
• calculus
• technology

Acknowledgements

The authors would like to thank Damir and Ozren Jungic for their helpful comments and suggestions on various drafts of this article. The authors would also like to acknowledge the IRMACS Centre at Simon Fraser University for its support.

Notes

1. Dr Lachlan is professor emeritus at the Department of Mathematics, Simon Fraser University, Burnaby, British Columbia.

2. Of course, we check these facts by using WolframAlpha or some other available tool.

3. Professor Lachlan told us that this was exactly what he did when he created the problem.

4. The instructor's choice of the subset of the set of tools based on their availability.