CONTENTS:- 1. Antiderivatives. 2. Integration by Parts. 3. Integration by Trignometrical Substitutions. 4. Integration of Hyperbolic. 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.
DESCRIPTION
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 endeavoring 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, Trignometrical 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 aspiring to successfully accomplish engineering and also those preparing for various competitive examinations are likely to find this book of much help.
