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Description:

Introduction to Integral Calculus develops an intellectually stimulating level of understanding of the subject while giving numerous applications and incorporating various scientific problems. The authors outline how to find volumes and lengths of curves, anti-differentiation, integration of trigonometric functions, integration by substitution, methods of substitution, the definite integral, methods for evaluating definite integrals, differential equations and their solutions, and ordinary differential equations of first order and first degree. This book is an immensely accessible go-to resource that maintains the highest standards for those in this field.

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Book details

List price: $78.95 Copyright year: 2012 Publisher: John Wiley & Sons, Limited Publication date: 2/9/2012 Binding: Hardcover Pages: 432 Size: 6.25" wide x 9.00" long x 1.25" tall Weight: 1.628 Language: English

AuthorTable of Contents

Foreword

Preface

Biographies

Introduction

Acknowledgment

Antiderivative(s) [or Indefinite Integral(s)]

Introduction

Useful Symbols, Terms, and Phrases Frequently Needed

Table(s) of Derivatives and their corresponding Integrals

Integration of Certain Combinations of Functions

Comparison Between the Operations of Differentiation and Integration

Integration Using Trigonometric Identities

Introduction

Some Important Integrals Involving sin x and cos x

Integrals of the Form (dx/(a sin x + b cos x)), where a, b r

Integration by Substitution: Change of Variable of Integration

Introduction

Generalized Power Rule

Theorem

To Evaluate Integrals of the Form , where a, b, c, and d are constant

Further Integration by Substitution: Additional Standard Integrals

Introduction

Special Cases of Integrals and Proof for Standard Integrals

Some New Integrals

Four More Standard Integrals

Integration by Parts

Introduction

Obtaining the Rule for Integration by Parts

Helpful Pictures Connecting Inverse Trigonometric Functions with Ordinary Trigonometric Functions

Rule for Proper Choice of First Function

Further Integration by Parts: Where the Given Integral Reappears on Right-Hand Side

Introduction

An Important Result: A Corollary to Integration by Parts

Application of the Corollary to Integration by Parts to Integrals that cannot be Solved Otherwise

Simpler Method(s) for Evaluating Standard Integrals

To Evaluate

Preparation for the Definite Integral: The Concept of Area

Introduction

Preparation for the Definite Integral

The Definite Integral as an Area

Definition of Area in Terms of the Definite Integral

Riemann Sums and the Analytical Definition of the Definite Integral

The Fundamental Theorems of Calculus

Introduction

Definite Integrals

The Area of Function A(x)

Statement and Proof of the Second Fundamental Theorem of Calculus

Differentiating a Definite Integral with Respect to a Variable Upper Limit

The Integral Function Identified as lnx or log<sub>e</sub>x

Introduction

Definition of Natural Logarithmic Function

The Calculus of lnx

The Graph of the Natural Logarithmic Function lnx

The Natural Exponential Function [exp(x) or e<sup>x</sup>]

Methods for Evaluating Definite Integrals

Introduction

The Rule for Evaluating Definite Integrals

Some Rules (Theorems) for Evaluation of Definite Integrals

Method of Integration by Parts in Definite Integrals

Some Important Properties of Definite Integrals

Introduction

Some Important Properties of Definite Integrals

Proof of Property (P<sub>0</sub>)

Proof of Property (P<sub>5</sub>)

Definite Integrals: Types of Functions

Applying the Definite Integral to Compute the Area of a Plane Figure

Introduction

Computing the Area of a Plane Region

Constructing the Rough Sketch [Cartesian Curves]

Computing the Area of a Circle (Developing Simpler Techniques)

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

Introduction

Methods of Integration

Equation for the Length of a Curve in Polar Coordinates

Solids of Revolution

Formula for the Volume of a "Solid of Revolution"

Area(s) of Surface(s) of Revolution

Differential Equations: Related Concepts and Terminology

Introduction

Important Formal Applications of Differentials (dy and dx)

Formation of a Differential Equation from a Given Relation, Involving Variables and the Essential Arbitrary Constants (or Parameters)

General Procedure for Eliminating "Two" Independent Arbitrary Constants (Using the Concept of Determinant)

The Simplest Type of Differential Equations

Methods of Solving Ordinary Differential Equations of the First Order and of the First Degree

Introduction

Methods of Solving Differential Equations

Linear Differential Equations

Type III: Exact Differential Equations

Applications of Differential Equations

INDEX

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