How to Integrate It
How to Integrate It
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.
- A systematic introduction to integration, containing many fully worked examples to demonstrate how the techniques are applied in practice
- Contains more than 500 exercises ranging in difficulty, from warm-ups to challenging extensions
- Accessible and engaging, this book will be of interest to students, teachers and self-learners
Reviews & endorsements
'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
Product details
December 2017Paperback
9781108408196
378 pages
227 × 151 × 21 mm
0.55kg
24 b/w illus. 20 tables 520 exercises
Available
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.
