242 HW & Materials

Chapter 5: Integration

5.6: Substitution and Area Between Curves

15-47 odd , 49 , 51 , 55 , 57 , 61 , 65 , 69 , 73 , 81 , 85 , 87 , 89 , 91 , 93 , 99 , 101 , 109 , 114 , 117
(Video) Area Between Curves: Development
(Video) Area Between Curves: Example
(Video) U-Substitution: Changing Limits
(Video) Linear U-Substitution

Chapter 6: Applications of Definite Integrals

6.1: Volumes Using Cross-Sections

17 , 19 , 23 , 25 , 27 , 31 , 33 , 37 , 39 , 45 , 49 , 51 , 55 , 57 , 61 , 65
(Video) Volume By Cross-Sections - Development
(Video) Volume By Cross-Sections - Example Disc
(Video) Volume By Cross-Sections - Example Washer

6.2: Volumes Using Cylindrical Shells

1 , 5 , 9 , 13 , 15 , 17 , 19 , 25 , 27 , 39 , 41 , 43 , 47
Demonstration
(Video) Volume By Cylindrical Shells - Development
(Video) Volume By Cylindrical Shells - Example 1
(Video) Volume By Cylindrical Shells - Example 2

6.3: Arc Length

1 , 5 , 9 , 13 , 15 , 25 , 27 , 29 , 33 , 35
(Video) Arc Length - Development
(Video) Arc Length - Example (Video) Arc Length Function
(Video) Arc Length Differential

6.4: Area of Surfaces of Revolution

13 , 15 , 17 , 19 , 21 , 25 , 29 , 31
(Video) Surface Area - Development
(Video) Surface Area - Example

6.5: Work and Fluid Force

1 , 5 , 7 , 11 , 17 , 19 , 21 , 31 , 33 , 37 , 41 , 43 , 45 , 46 , 47 , 49
(Video) Physics Basics
(Video) Work
(Video) Work on a Spring - Development
(Video) Work on a Spring - Example
(Video) Work - Pumping Liquid
(Video) Fluid Force - Development
(Video) Fluid Force - Example

Chapter 8: Integration Techniques

8.2: Integration by Parts

1 , 3 , 5 , 9 , 11 , 13 , 17 , 21 , 23 , 25 , 29 , 33 , 37 , 43 , 47 , 51 , 55 , 57 , 59 , 63 , 65
(Video) Integration by Parts - Development
(Video) Integration by Parts - Example
(Video) Integration by Parts - Table Method
(Video) Integration by Parts - Unorthodox Example

8.3: Trigonometric Integrals

3 , 7 , 15 , 19 , 23 , 25 , 33 , 39 , 45 , 47 , 51 , 63 , 67 , 71
(Video) Powers of Sine and Cosine - Odd
(Video) Powers of Sine and Cosine - Even
(Video) Powers of Tangent
(Video) Powers of Secant - Even
(Video) Powers of Secant - Odd
(Video) Product of Sine and Cosine - Differing Angles

8.4: Trigonometric Substitutions

1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 , 23 , 31 , 53 , 55 , 58 , 62
(Video) Using Sine
(Video) Using Tangent
(Video) Using Secant

8.5: Integration of Rational Functions by Partial Fractions

9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 33 , 37 , 57 , 61 , 63 , 73
(Video) Linear Non-Repeated Factors
(Video) Linear Non-Repeated Factors - Shortcut
(Video) Linear Repeated Factors
(Video) Quadratic Non-Repeated Factors
(Video) Quadratic Repeated Factors

4.5: Indeterminant Forms and L'Hopital's Rule

3 , 13 , 15 , 19 , 23 , 27 , 29 , 31 , 35 , 41 , 49 , 51 , 53 , 59 , 63 , 65 , 67 , 79 , 85
(Video) Form 0/0
(Video) Form \( \infty / \infty \)
(Video) Form \( (0)(\infty) \)
(Video) Form \( \infty - \infty \)
(Video) Exponential Form

8.8: Improper Integrals

Part 1: 1 , 3 , 5 , 11 , 13 , 19 , 23 , 25 , 29 , 33
(Video) Improper Integral at \( \infty \)
(Video) Improper Integral at \( - \infty \)
(Video) Improper Integral - All Reals
(Video) Improper Integrals at Discontinuities
Part 2: 51 , 53 , 55 , 57 , 59 , 61 , 65 , 67 , 73 , 81 , 82 , 85
(Video) P-Integrals
(Video) Comparisons with \( \ln (x) \)
(Video) DCT - Development
(Video) DCT - Example - Convergent
(Video) DCT - Example - Divergent
(Video) LCT - Development
(Video) LCT - Example

Chapter 10: Infinite Sequences and Series

Style Guide for Series Conv./Div. Arguments

10.1: Sequences

4 , 11 , 13 , 15 , 21 , 23 , 31 , 35 , 41 , 43 , 45 , 47 , 57 , 59 , 63 , 67 , 71 , 73 , 83 , 109 , 116 , 123
(Video) Sequence & Series
(Video) Convergence for Sequences
(Video) Sequence Divergence to \(\infty\)
(Video) Limit Properties for Sequences
(Video) Sandwich Thm. for Sequences
(Video) Thm. 4 Sequences
(Video) Thm. 5 Sequences
(Video) Monotonic & Bounded Sequences

10.2: Infinite Series

7 , 11 , 19 , 21 , 23 , 26 , 27 , 31 , 35 , 39 , 41 , 43 , 45 , 53 , 63 , 65 , 67 , 77 , 79 , 103 , 104
(Video) Series
(Video) Geometric Series
(Video) Geometric Series - Example
(Video) Telescopng Series
(Video) N-th Term Test
(Video) Series Properties
(Video) Useful Facts for Series

10.3: The Integral Test

1 , 5 , 9 , 13 , 17 , 29 , 31 , 33 , 37 , 41 , 55 , 56 , 57 , 58 , 59 , 63
(Video) Integral Test - Development
(Video) Integral Test - Example
(Video) P-Series
(Video) Truncation Error - Development
(Video) Truncation Error - Example

10.4: Comparison Tests

17 , 19 , 23 , 25 , 27 , 35 , 37 , 39 , 49 , 53 , 58 , 60
(Video) Series DCT - Development
(Video) Series DCT - Convergent Example
(Video) Series LCT - Development
(Video) Series LCT - Example

10.5: The Ratio and Root Test

17 , 19 , 23 , 25 , 31 , 35 , 37 , 41 , 47, 49 , 55 , 67 , 69
(Video) Absolute Convergence - Definition
(Video) ACT - Development
(Video) ACT - Example
(Video) Ratio Test - Development Part 1
(Video) Ratio Test - Development Part 2
(Video) Ratio Test - Example
(Video) Root Test - Development
(Video) Root Test - Example

10.6: Alternating Series, Absolute and Conditional Convergence

1 , 3 , 7 , 11 , 15 , 23 , 27 , 29 , 33 , 41 , 47 , 49 , 50 , 51 , 53 , 54 , 55 , 57 , 59 , 63 , 71 , 96
(Video) AST - Development & Example
(Video) AST - Fail
(Video) Alt. Series Estimation Thm.

10.7: Power Series

3 , 5 , 7 , 11 , 13 , 15 , 17 , 23 , 29 , 31 , 37 , 39 , 41 , 55 , 57 , 61 , 64
(Video) Power Series - Introduction
(Video) Power Series - Example - Finite Interval
(Video) Power Series - Example - All Reals
(Video) Power Series - Example - Single Point
(Video) Term-By-Term Differentiation Thm.

10.8: Taylor and MacLauren Series

1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 , 25 , 29 , 31 , 35
Taylor Polynomial Demonstration
CORDIC Demonstration
(Video) Taylor Series - Introduction
(Video) Taylor Series - Development
(Video) Taylor Series - \( e^x \)
(Video) Taylor Series - \( \sin (x) \)

10.9: Convergence of Taylor Series

1 , 7 , 9 , 13 , 21 , 28 , 31 , 39 , 41 , 43 , 45 , 46 , 47 , 49
(Video) Taylor's Theorem
(Video) Error Bounds for Taylor Polynomial Approximations
(Video) Convergence of the Taylor Series for \( \sin(x) \)
(Video) Convergence of the Taylor Series for \( e^x \)

10.10: The Binomial Series and Applications of Taylor Series

1 , 7 , 15 , 17 , 19 , 21 , 23 , 29 , 31 , 33 , 37 , 41 , 45 , 49 , 59 , 67 , 69
(Video) Binomial Series
(Video) Evaluating Limits Using Taylor Series
(Video) Approximating Definite Integrals Using Taylor Series

Chapter 11: Parametric Equations and Polar Coordinates

11.1: Parametrizations of Plane Curves

1 , 3 , 5 , 7 , 9 , 11 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , 31 , 32 , 33
(Video) Parametric Equations - Introduction
(Video) Non-Uniqueness of Parametrizations
(Video) Parametrizing a Circle
(Video) Parametrizing a Line

11.2: Calculus with Parametric Curves

1 , 5 , 7 , 9 , 13 , 17 , 21 , 23 , 25 , 27 , 29 , 31 , 33 , 41 , 47
(Video) Slope of a Parametric Curve
(Video) Higher Order Derivatives
(Video) Surface Area of Revolution of a Parametric Curve
(Video) Area Under a Parametric Curve

11.3: Polar Coordinates

1 , 7 , 11 , 15 , 19 , 23 , 27 , 29 , 31 , 33 , 39 , 43 , 51 , 55 , 57, 59 , 59 , 65 , 67
(Video) Polar Coordinates - Introduction
(Video) Polar Curve - \( r = \sin \theta \)
(Video) Polar Curve - Cardiod

11.4: Graphing in Polar Coordinates

1 , 5 , 7 , 9 , 13 , 17 , 18 , 19 , 20 , 25 , 27
(Video) Slope of a Polar Curve
Explore Polar Graphs

11.5: Areas and Lengths in Polar Coordinates

1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27
(Video) Area in Polar Coordinates
(Video) Polar Area - Example 1
(Video) Polar Area - Example 2
(Video) Polar Area - Example 3
(Video) Polar Length - Development
(Video) Polar Length - Example