Integration for Calculus, Analysis, and Differential Equations

The book assists Calculus students to gain a better understanding and command of integration and its applications. It reaches to students in more advanced courses such as Multivariable Calculus, Differential Equations, and Analysis, where the ability to effectively integrate is essential for their success.

Keeping the reader constantly focused on the three principal epistemological questions: "What for?", "Why?", and "How?", the book is designated as a supplementary instructional tool and consists of
9 Chapters treating the three kinds of integral: indefinite, definite, and improper. Also covering various aspects of integral calculus from abstract definitions and theorems (with complete proof whenever appropriate) through various integration techniques to applications,3 Appendices containing a table of basic integrals, reduction formulas, and basic identities of algebra and trigonometry.
It also contains
143 Examples, including 112 thoughtfully selected Problems with complete step-by-step solutions, the same problem occasionally solved in more than one way while encouraging the reader to find the most efficient integration path, and6 Exercises, 162 Practice Problems offered at the end of each chapter starting with Chapter 2 as well as 30 Mixed Integration Problems "for dessert", where the reader is expected to independently choose and implement the best possible integration approach.
The Answers to all the 192 Problems are provided in the Answer Key. The book will benefit undergraduates, advanced undergraduates, and members of the public with an interest in science and technology, helping them to master techniques of integration at the level expected in a calculus course.
Sample Chapter(s)
Chapter 1: Indefinite and Definite Integrals

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Contents:PrefaceIndefinite and Definite IntegralsDirect IntegrationMethod of SubstitutionMethod of Integration by PartsTrigonometric IntegralsTrigonometric SubstitutionsIntegration of Rational FunctionsRationalizing SubstitutionsCan We Integrate Them All Now?Improper IntegralsMixed Integration ProblemsAnswer KeyAppendices:Table of Basic IntegralsReduction FormulasBasic Identities of Algebra and TrigonometryBibliographyIndex
Readership: Undergraduates, advanced undergraduates and members of the public with an interest in integration and its applications.Indefinite Integral;Definite Integral;Improper Integral;Direct Integration;Method of Substitution;Integration by Parts0Key Features:The book contains a wealth of examples and thoughtfully selected problems with complete step-by-step solutions, while providing several methods of solving the same problemA chapter dedicated to direct integration, i.e. integration, which, using the integration rules alone, reduces the integral of a given function to a combination of table integrals and making no use of any special integration techniques