How to Integrate It: A Practical Guide to Finding Elementary Integrals
Cambridge University Press, 12/21/2017
EAN 9781108418812, ISBN10: 1108418813
Hardcover, 378 pages, 23.5 x 15.6 x 2.5 cm
Language: English
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 À 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.
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.