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.

Promotional Information

Practical guide demystifying the art of integration for beginning calculus students through thorough explanations, examples and exercises.

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).

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