Integral Calculus (Paperback)  | Released: 2005

The present book Integral Calculus is a unique textbook on Integration, aiming at providing a fairly complete account of the basic concepts required to build a strong foundation for a student endeavouring to study this subject. The analytical approach to the major concepts makes the book highly self-contained and comprehensive guide that succeeds in making the concepts easily understandable. These concepts include Integration by Substitution Method, Parts, Trigonometrical Substitutions and Partial Functions; Integration of Hyperbolic Functions, Rational Functions, Irrational Functions and Transcendental Functions; Definite Integrals; Reduction Formulae; Beta and Gamma Functions; Determination of Areas, Lengths, Volumes and Surfaces of Solids of Revolution and many more. All the elementary principles and fundamental concepts have been explained rigorously, leaving no scope for illusion or confusion. The focus throughout the text has been on presenting the subject matter in a well-knit manner and lucid style, so that even a student with average mathematical skill would find it accessible to himself. In addition, the book provides numerous well-graded solved examples, generally set in various university and competitive examinations, which will facilitate easy understanding besides acquainting the students with a variety of questions. It is hoped that the book would be highly useful for the students and teachers of Mathematics. Students aspiring to successfully accomplish engineering and also those preparing for various competitive examinations are likely to find this book of much help.Table of Contents: 1. Antiderivatives 2. Integration by Substitution Method 3. Integration by Parts 4. Integration by Trigonometrical Substitutions 5. Integration of Hyperbolic Functions 6. Integration of Rational Functions 7. Integration of Irrational Functions 8. Integration by Partial Fractions 9. Integration of Transcendental Functions 10. Definite Integrals 11. Reduction Formulae 12. Beta and Gamma Functions 13. Determination of Areas (Quadrature) 14. Determination of Lengths (Rectification) 15. Determination of Volumes and Surfaces of Solids of Revolution 16. Integration of Functions of Two and Three Variables 17. Change of Order of Integration