An accessible introduction to the fundamentals of calculusneeded to solve current problems in engineering and the physicalsciencesI ntegration is an important function of calculus, andIntroduction to Integral Calculus combines fundamental conceptswith scientific problems to develop intuition and skills forsolving mathematical problems related to engineering and thephysical sciences. The authors provide a solid introduction tointegral calculus and feature applications of integration,solutions of differential equations, and evaluation methods. Withlogical organization coupled with clear, simple explanations, theauthors reinforce new concepts to progressively build skills andknowledge, and numerous real-world examples as well as intriguingapplications help readers to better understand the connectionsbetween the theory of calculus and practical problem solving.The first six chapters address the prerequisites needed tounderstand the principles of integral calculus and explore suchtopics as anti-derivatives, methods of converting integrals intostandard form, and the concept of area. Next, the authors reviewnumerous methods and applications of integral calculus,including:* Mastering and applying the first and second fundamental theoremsof 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 solveordinary differential equationsWith this book as their guide, readers quickly learn to solve abroad range of current problems throughout the physical sciencesand engineering that can only be solved with calculus. Examplesthroughout provide practical guidance, and practice problems andexercises allow for further development and fine-tuning of variouscalculus skills. Introduction to Integral Calculus is an excellentbook for upper-undergraduate calculus courses and is also an idealreference for students and professionals who would like to gain afurther understanding of the use of calculus to solve problems in asimplified manner.

FOREWORD ixPREFACE 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 Integrals71.4 Integration of Certain Combinations of Functions 101.5 Comparison Between the Operations of Differentiation andIntegration 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, bepsilon r 373a Integration by Substitution: Change of Variable ofIntegration 433b Further Integration by Substitution: Additional StandardIntegrals 674a Integration by Parts 974b Further Integration by Parts: Where the Given IntegralReappears on Right-Hand Side 1175 Preparation for the Definite Integral: The Concept of Area1395.1 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 DefiniteIntegral 1516a The Fundamental Theorems of Calculus 1656b The Integral Function D 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 aPlane Figure 2498b To Find Length(s) of Arc(s) of Curve(s), the Volume(s) ofSolid(s) of Revolution, and the Area(s) of Surface(s) of Solid(s)of Revolution 2959a Differential Equations: Related Concepts and Terminology3219a.4 Definition: Integral Curve 3329b Methods of Solving Ordinary Differential Equations of theFirst Order and of the First Degree 361INDEX 399