Chapter 6: Applications of Integration

Section 
Topic 
6.1 
Areas Between Curves
6.1.18 Areas Between Curves
6.1.38 Areas Between Curves
6.1.42 Areas Between Curves

6.2 
Volumes
6.2.8 Volumes
6.2.12 Volumes
6.2.17 Volumes
6.2.34 Volumes
6.2.48 Volumes
6.2.56 Volumes

6.3 
Volumes by Cylindrical Shells
6.3.12 Volumes by Cylindrical Shells
6.3.18 Volumes by Cylindrical Shells
6.3.20 Volumes by Cylindrical Shells
6.3.39 Volumes by Cylindrical Shells

6.4 
Work
6.4.10 Work
6.4.14 Work
6.4.18 Work
6.4.24 Work
6.4.26 Work
6.4.34 Work

6.5 
Average Value of a Function
6.5.8 Average Value of a Function
6.5.16 Average Value of a Function
6.5.18 Average Value of a Function



Chapter 7: Techniques of Integration 
Section 
Topic 
7.1 
Integration by Parts
7.1.22 Integration by Parts
7.1.40 Integration by Parts
7.1.63 Integration by Parts

7.2 
Trigonometric Integrals
7.2.22 Trigonometric Integrals
7.2.38 Trigonometric Integrals
7.2.66 Trigonometric Integrals

7.3 
Trigonometric Substitution
7.3.8 Trigonometric Substitution
7.3.20 Trigonometric Substitution
7.3.26 Trigonometric Substitution
7.3.30 Trigonometric Substitution
7.3.42 Trigonometric Substitution

7.4 
Integration of Rational Functions by Partial Fractions
7.4.8 Integration of Rational Functions by Partial Fractions
7.4.12 Integration of Rational Functions by Partial Fractions
7.4.20 Integration of Rational Functions by Partial Fractions
7.4.28 Integration of Rational Functions by Partial Fractions
7.4.48 Integration of Rational Functions by Partial Fractions
7.4.67 Integration of Rational Functions by Partial Fractions
7.4.70 Integration of Rational Functions by Partial Fractions

7.5 
Strategy for Integration 
7.6 
Integration Using Tables and Computer Algebra Systems
7.6.20 Integration Using Tables and Computer Algebra Systems
7.6.26
Integration Using Tables and Computer Algebra Systems
7.6.44
Integration Using Tables and Computer Algebra Systems
7.6.46
Integration Using Tables and Computer Algebra Systems

7.7 
Approximate Integration
7.7.14 Approximate Integration
7.7.24
Approximate Integration
7.7.36
Approximate Integration
7.7.40
Approximate Integration

7.8 
Improper Integrals
7.8.16 Improper Integrals
7.8.30
Improper Integrals
7.8.48
Improper Integrals
7.8.70
Improper Integrals



Chapter 8: Further Applications of Integration 
Section 
Topic 
8.1 
Arc Length
8.1.6 Arc Length
8.1.14 Arc Length
8.1.28 Arc Length
8.1.36 Arc Length

8.2 
Area of a Surface of Revolution
8.2.4 Area of a Surface of Revolution
8.2.10 Area of a Surface of Revolution
8.2.18 Area of a Surface of Revolution
8.2.26 Area of a Surface of Revolution

8.3 
Applications to Physics and Engineering
8.3.4 Applications to Physics and Engineering
8.3.10 Applications to Physics and Engineering
8.3.28 Applications to Physics and Engineering
8.3.47 Applications to Physics and Engineering

8.4 
Applications to Economics and Biology
8.4.2 Applications to Economics and Biology
8.4.8 Applications to Economics and Biology
8.4.15,16 Applications to Economics and Biology
8.4.20 Applications to Economics and Biology

8.5 
Probability
8.5.4 Probability
8.5.12 Probability
8.5.16 Probability



Chapter 9: Differential Equations 
Section 
Topic 
9.1 
Modeling with Differential Equations
9.1.6 Modeling with Differential Equations
9.1.10 Modeling with Differential Equations

9.2 
Direction Fields and Euler’s Method
9.2.2 Direction Fields and Euler's Method
9.2.14 Direction Fields and Euler's Method
9.2.24 Direction Fields and Euler's Method

9.3 
Separable Equations
9.3.8 Separable Equations
9.3.16 Separable Equations
9.3.28 Separable Equations
9.3.30 Separable Equations
9.3.48 Separable Equations
9.3.54 Separable Equations

9.4 
Models for Population Growth
9.4.10 Models for Population Growth
9.4.16 Models for Population Growth
9.4.22 Models for Population Growth

9.5 
Linear Equations
9.5.10 Linear Equations
9.5.18 Linear Equations
9.5.34 Linear Equations

9.6 
PredatorPrey Systems
9.6.4 PredatorPrey Systems
9.6.6 PredatorPrey Systems
9.6.10 PredatorPrey Systems



Chapter 10: Parametric Equations and Polar Coordinates 
Section 
Topic 
10.1 
Curves Defined by Parametric Equations
10.1.8 Curves Defined by Parametric Equations
10.1.18 Curves Defined by Parametric Equations
10.1.40 Curves Defined by Parametric Equations

10.2 
Calculus with Parametric Curves
10.2.6 Calculus with Parametric Curves
10.2.14 Calculus with Parametric Curves
10.2.24 Calculus with Parametric Curves
10.2.34 Calculus with Parametric Curves
10.2.44 Calculus with Parametric Curves
10.2.58 Calculus with Parametric Curves

10.3 
Polar Coordinates
10.3.14 Polar Coordinates
10.3.16 Polar Coordinates
10.3.26 Polar Coordinates
10.3.40 Polar Coordinates
10.3.64 Polar Coordinates
10.3.70 Polar Coordinates

10.4 
Areas and Lengths in Polar Coordinates
10.4.6 Areas and Lengths in Polar Coordinates
10.4.16 Areas and Lengths in Polar Coordinates
10.4.26 Areas and Lengths in Polar Coordinates
10.4.40 Areas and Lengths in Polar Coordinates

10.5 
Conic Sections 
10.6 
Conic Sections in Polar Coordinates 


Chapter 11: Infinite Sequences and Series 
Section 
Topic 
11.1 
Sequences
11.1.20 Sequences
11.1.22 Sequences
11.1.30 Sequences
11.1.36 Sequences
11.1.58 Sequences
11.1.62 Sequences
11.1.74 Sequences
11.1.90 Sequences

11.2 
Series
11.2.4 Series
11.2.8 Series
11.2.12 Series
11.2.18 Series
11.2.26 Series
11.2.30 Series
11.2.38 Series
11.2.46 Series
11.2.58 Series
11.2.72 Series

11.3 
The Integral Test and Estimates of Sums
11.3.8 The Integral Test and Estimates of Sums
11.3.14 The Integral Test and Estimates of Sums
11.3.20 The Integral Test and Estimates of Sums

11.4 
The Comparison Tests
11.4.6 The Comparison Tests
11.4.20 The Comparison Tests
11.4.30 The Comparison Tests
11.5.34 The Comparison Tests

11.5 
Alternating Series
11.5.6 Alternating Series
11.5.12 Alternating Series
11.5.22 Alternating Series
11.5.26 Alternating Series
11.5.30 Alternating Series

11.6 
Absolute Convergence and the Ratio and Root Tests
11.6.4 Absolute Convergence and the Ratio and Root Tests
11.6.10 Absolute Convergence and the Ratio and Root Tests
11.6.22 Absolute Convergence and the Ratio and Root Tests
11.6.28 Absolute Convergence and the Ratio and Root Tests
11.6.36 Absolute Convergence and the Ratio and Root Tests
11.6.46,48 Absolute Convergence and the Ratio and Root Tests

11.7 
Strategy for Testing Series 
11.8 
Power Series
11.8.6 Power Series
11.8.8 Power Series
11.8.16 Power Series
11.8.24 Power Series
11.8.36 Power Series

11.9 
Representation of Functions as Power Series
11.9.4 Representation of Functions as Power Series
11.9.10 Representation of Functions as Power Series
11.9.18 Representation of Functions as Power Series
11.9.26 Representation of Functions as Power Series

11.10 
Taylor and
Maclaurin Series
11.10.10 Taylor and Maclaurin Series
11.10.16 Taylor and Maclaurin Series
11.10.24 Taylor and Maclaurin Series
11.10.32 Taylor and Maclaurin Series
11.10.40 Taylor and Maclaurin Series
11.10.60 Taylor and Maclaurin Series
11.10.78 Taylor and Maclaurin Series 
11.11 
Applications of Taylor Polynomials
11.11.08 Applications of Taylor Polynomials
11.11.18 Applications of Taylor Polynomials
11.11.28 Applications of Taylor Polynomials
11.11.38 Applications of Taylor Polynomials 