How to Integrate It: A Practical Guide to Finding Elementary Integrals

by Seán M. Stewart

Overview

While differentiating elementary functions is merely a skill, finding their integrals is an art. This practical introduction to the art of integration gives readers the tools and confidence to tackle common and uncommon integrals. After a review of the basic properties of the Riemann integral, each chapter is devoted to a particular technique of elementary integration. Thorough explanations and plentiful worked examples prepare the reader for the extensive exercises at the end of each chapter. These exercises increase in difficulty from warm-up problems, through drill examples, to challenging extensions which illustrate such advanced topics as the irrationality of π and e, the solution of the Basel problem, Leibniz's series and Wallis's product. The author's accessible and engaging manner will appeal to a wide audience, including students, teachers and self-learners. The book can serve as a complete introduction to finding elementary integrals, or as a supplementary text for any beginning course in calculus.

Product Details

ISBN-13:	9781108408196
Publisher:	Cambridge University Press
Publication date:	12/21/2017
Pages:	378
Product dimensions:	5.94(w) x 8.94(h) x 0.83(d)

About the Author

Seán M. Stewart is the co-founder and principal teaching fellow at Omegadot Tuition, Sydney. He has had over eighteen years of experience teaching mathematics and physics at both the secondary and tertiary levels. He is a member of numerous professional associations and societies in mathematics and physics. In 2004, he won the Petroleum Institute Outstanding Faculty Award for Teaching. He has written numerous research articles and co-authored the book Blackbody Radiation: A History of Thermal Radiation Computational Aids and Numerical Methods (2016).

Table of Contents

1. The Riemann integral; 2. Basic properties of the definite integral – Part I; 3. Some basic standard forms; 4. Basic properties of the definite integral – Part II; 5. Standard forms; 6. Integration by substitution; 7. Integration by parts; 8. Trigonometric integrals; 9. Hyperbolic integrals; 10. Trigonometric and hyperbolic substitutions; 11. Integrating rational functions by partial fraction decomposition; 12. Six useful integrals; 13. Inverse hyperbolic functions and integrals leading to them; 14. Tangent half-angle substitution; 15. Further trigonometric integrals; 16. Further properties for definite integrals; 17. Integrating inverse functions; 18. Reduction formulae; 19. Some other special techniques and substitutions; 20. Improper integrals; 21. Two important improper integrals; Appendix A. Partial fractions; Appendix B. Answers to selected exercises; Index.

Editorial Reviews

'Each chapter of this book starts with a quote, then a little motivating introduction or example, followed by a definition, a rule or some properties, then a wealth of practical examples and exercises which range in difficulty. … The chapters concerned with the integration techniques are finely written: they are short with minimal theoretical explanation, good practical rules, and a great number of examples and exercises. Students and teachers can find a lot of interesting things to learn or use. … This book is a very good introduction to the techniques of integration. It is not a theoretical book on integration; indeed, most of it can be well understood by pre-university students who are learning integral calculus.' Mathematical Association of America

'This is a book for those who love to integrate, especially indefinite integrals … Plenty of exercises, both routine and challenging, are included.' M. Bona, Choice

From the Publisher