This book gives a straightforward introduction to techniques of integration, which is one of the most difficult areas of calculus. It is well known that the only way to learn calculus is by solving problems. About 200 completely worked examples are used to introduce methods of integration and to demonstrate problem-solving techniques. The sections are written as self-guided tutorials. Each chapter opens with appropriate definitions and formulas followed by a lot of solved problems listed in order of increasing difficulty.
Topics include: The Indefinite Integral and Basic Formulas of Integration, Method of Substitution, Integration by Parts, Integration of Rational Functions, Integration of Irrational Functions, Integration of Rational Expressions of Trigonometric Functions, Integrals of Powers and Products of Sine and Cosine, Integrals Involving Powers of Other Trigonometric Functions, Integration of Hyperbolic Functions, Using Trigonometric and Hyperbolic Substitutions, The Definite Integral and Fundamental Theorem of Calculus, Improper Integral.
Studying and solving these problems improves understanding of techniques of integration and helps students to pass exams in the fastest, most efficient manner available.