Introduction to Integral Calculus

ULRICH L. ROHDE, PhD, ScD, Dr-Ing, is Chairman of Synergy Microwave Corporation, President of Communications Consulting Corporation, and a Partner of Rohde & Schwarz. A Fellow of the IEEE, Professor Rohde holds several patents and has published more than 200 scientific papers. G. C. JAIN, B.Sc., is a retired scientist from the Defense Research and Development Organization in India.AJAY K. PODDAR, PhD, is Chief Scientist at Synergy Microwave Corporation. A Senior Member of the IEEE, Dr. Poddar holds several dozen patents and has published more than 180 scientific papers.A. K. GHOSH, PhD, is Professor in the Department of Aerospace Engineering at the IIT Kanpur, India. He has published more than 120 scientific papers.

• FOREWORD ix PREFACE xiiiBIOGRAPHIES xxiINTRODUCTION xxiiiACKNOWLEDGMENT xxv1 Antiderivative(s) [or Indefinite Integral(s)] 11.1 Introduction 11.2 Useful Symbols, Terms, and Phrases Frequently Needed 61.3 Table(s) of Derivatives and their corresponding Integrals 71.4 Integration of Certain Combinations of Functions 101.5 Comparison Between the Operations of Differentiation and Integration 152 Integration Using Trigonometric Identities 172.1 Introduction 172.2 Some Important Integrals Involving sin x and cos x 342.3 Integrals of the Form ? (d/( a sin  + b cos x)), where a, b ϵ r 373a Integration by Substitution: Change of Variable of Integration 433b Further Integration by Substitution: Additional Standard Integrals 674a Integration by Parts 974b Further Integration by Parts: Where the Given Integral Reappears on Right-Hand Side 1175 Preparation for the Definite Integral: The Concept of Area 1395.1 Introduction 1395.2 Preparation for the Definite Integral 1405.3 The Definite Integral as an Area 1435.4 Definition of Area in Terms of the Definite Integral 1515.5 Riemann Sums and the Analytical Definition of the Definite Integral 1516a The Fundamental Theorems of Calculus 1656b The Integral Function Ð x 1 1 t dt, (x > 0) Identified as ln x or loge x 1837a Methods for Evaluating Definite Integrals 1977b Some Important Properties of Definite Integrals 2138a Applying the Definite Integral to Compute the Area of a Plane Figure 2498b To Find Length(s) of Arc(s) of Curve(s), the Volume(s) of Solid(s) of Revolution, and the Area(s) of Surface(s) of Solid(s) of Revolution 2959a Differential Equations: Related Concepts and Terminology 3219a.4 Definition: Integral Curve 3329b Methods of Solving Ordinary Differential Equations of the First Order and of the First Degree 361INDEX 399

“Introduction to Integral Calculus is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner.”  (Zentralblatt MATH, 2012)“Long on examples but often short of exercises, this work might best be used as a reference source.  Summing Up: Recommended.  Lower-and upper-division undergraduates.”  (Choice, 1 September 2012)