Chapter 5: THE INTEGRAL

Chapter Introduction

5.1 Approximating and Computing Area

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus, Part I

5.4 The Fundamental Theorem of Calculus, Part II

5.5 Net Change as the Integral of a Rate

5.6 Substitution Method

5.7 Further Transcendental Functions

5.8 Exponential Growth and Decay

Chapter 6: Applications of the Integral

Introduction

6.1 Area Between Two Curves

6.2 Setting Up Integrals: Volume, Density, Average Value

6.3 Volumes of Revolution

6.4 The Method of Cylindrical Shells

6.5 Work and Energy

Chapter 7: Techniques of Integration

Introduction

7.1 Integration by Parts

7.2 Trigonometric Integrals

7.3 Trigonometric Substitution

7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions

7.5 The Method of Partial Fractions

7.6 Improper Integrals

7.7 Probability and Integration

7.8 Numerical Integration

Chapter 8: Further Applications of the Integral and Taylor Polynomials

Introduction

8.1 Arc Length and Surface Area

8.2 Fluid Pressure and Force

8.3 Center of Mass

8.4 Taylor Polynomials

Chapter 9: Introduction to Differential Equations

Introduction

9.1 Solving Differential Equations

9.2 Models Involving \(y' = k (y - b)\)

9.3 Graphical and Numerical Methods

9.4 The Logistic Equation

9.5 First-Order Linear Equations

Chapter 10: Infinite Series

Introduction

10.1 Sequences

10.2 Summing an Infinite Series

10.3 Convergence of Series with Positive Terms

10.4 Absolute and Conditional Convergence

10.5 The Ratio and Root Tests

10.6 Power Series

10.7 Taylor Series