On that most over Skinned of Improper Integrals

Summary

Continuing a much discussed topic of the various ways a particular improper integral can be evaluated, we give three further ways its generalization can be evaluated. Using techniques typically encountered immediately after the calculus sequence of courses we show how the improper integral can be evaluated using the beta and gamma functions, by first converting it to a double integral, and using a property of the Laplace transform.

Acknowledgment

The author would like to thank the two anonymous referees for helpful suggestions on an earlier draft of this paper.

Additional information

Notes on contributors

Seán M. Stewart

Seán M. Stewart ([email protected]) received his Ph.D. in theoretical physics from the University of Wollongong. After briefly working in Australia, he for many years taught mathematics and physics to engineers in Kazakhstan and the United Arab Emirates. He now lectures at King Abdullah University of Science and Technology in Saudi Arabia. He has always found it hard to resist the challenge of a definite integral and is the author of How to Integrate It: A Practical Guide to Finding Elementary Integrals published by Cambridge University Press.