Table of Contents

Chapter 1 • Integration
 Riemann Sums
 Riemann Sums and Sigma Notation
 Definite Integrals as Limits of Riemann Sums
 The Fundamental Theorem of Calculus: Evaluating Definite Integrals
 Average Value of a Function
 The Fundamental Theorem of Calculus: Functions Defined by Integrals
 The Net Change Theorem
 Properties of Definite Integrals
 Integration by Substitution: Indefinite Integrals

Chapter 2 • Applications of Integration
 Area between a Curve and a Line
 Area between Curves
 Volumes of Solids of Revolution Using the Disk and Washer Methods
 Volumes of Solids of Revolution Using the Shell Method
 Arc Length by Integration
 Indefinite Integrals: Exponential and Reciprocal Functions
 Integrals Resulting in Logarithmic Functions
 Exponential Growth and Decay Models
 Exponential Growth and Decay

Chapter 3 • Techniques of Integration
 Integration by Parts
 Trigonometric Integrals
 Integration by Trigonometric Substitutions
 Integration by Partial Fractions with Linear Factors
 Integration by Partial Fractions with Quadratic Factors
 Numerical Integration: Simpson’s Rule
 Numerical Integration: The Trapezoidal Rule
 Numerical Integration: Riemann Sums
 Improper Integrals: Infinite Limits of Integration
 Improper Integrals: Discontinuous Integrands
 Comparison Test for Improper Integrals
 Chapter 4 • Introduction to Differential Equations
 Chapter 5 • Sequences and Series
 Chapter 6 • Power Series

Chapter 7 • Parametric Equations and Polar Coordinates
 Parametric Equations and Curves in Two Dimensions
 Derivatives of Parametric Equations
 Area Enclosed by Parametric Curves
 Arc Length of Parametric Curves
 Surface of Revolution of Parametric Curves
 Second Derivatives of Parametric Equations
 Polar Coordinates
 Graphing Polar Curves
 Arc Length of a Polar Curve
 Equation of a Parabola
 Equation of an Ellipse
 Identifying Conic Sections