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
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
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
Introduction
8.1 Arc Length and Surface Area
8.2 Fluid Pressure and Force
8.3 Center of Mass
8.4 Taylor Polynomials
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
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