# Introduction to Integral Calculus: Systematic Studies with Engineering Applications for Beginners

John Wiley & Sons, Jan 20, 2012 - Mathematics - 428 pages
An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciences

I ntegration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The authors provide a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. With logical organization coupled with clear, simple explanations, the authors reinforce new concepts to progressively build skills and knowledge, and numerous real-world examples as well as intriguing applications help readers to better understand the connections between the theory of calculus and practical problem solving.

The first six chapters address the prerequisites needed to understand the principles of integral calculus and explore such topics as anti-derivatives, methods of converting integrals into standard form, and the concept of area. Next, the authors review numerous methods and applications of integral calculus, including:

• Mastering and applying the first and second fundamental theorems of calculus to compute definite integrals

• Defining the natural logarithmic function using calculus

• Evaluating definite integrals

• Calculating plane areas bounded by curves

• Applying basic concepts of differential equations to solve ordinary differential equations

With this book as their guide, readers quickly learn to solve a broad range of current problems throughout the physical sciences and engineering that can only be solved with calculus. Examples throughout provide practical guidance, and practice problems and exercises allow for further development and fine-tuning of various calculus skills. 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.

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### Contents

 Biographies iv Integration Using Trigonometric Identities ix Integration by Substitution Change of Variable 7 Further Integration by Substitution Additional 35 Integration by Parts 12 Further Integration by Parts Where the Given 34 Preparation for the Definite Integral The Concept 58 The Fundamental Theorems of Calculus 87
 Methods for Evaluating Definite Integrals 122 Some Important Properties of Definite Integrals 8 Applying the Definite Integral to Compute the Area 44 Techniques 44 To Find Lengths of Arcs of Curves 44 Differential Equations Related Concepts 44 Methods of Solving Ordinary Differential Equations 104 Index 139

 The Integral Function Identified as ln x 106

### About the author (2012)

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.