How to Integrate It

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

This practical guide demystifies the art of integration. Each chapter explains a particular technique of elementary integration through thorough explanations, worked examples and numerous exercises ranging from the routine to the challenging. It may serve as a complete introduction, or as a supplementary text for any beginning course in calculus.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.