Basic Integration and the Definite Integral
Ex:
Indefinite Integration with a Negative Exponent
Ex:
Indefinite Integration Involving a Product
Ex:
Indefinite Integration with a Variety of Terms
The Six
Basic Trigonometric Integration Formulas
Examples Using Basic Trig Integral Formulas: Part 1, Part 2
Integration Involving Inverse Trig Functions: Part 1, Part 2, Part 3
The
Definite Integral
Ex: Setting Up a Definite Integral To
Determine Area Under a Function
Ex: Property of Definite Integral
Subtraction
Ex: Property of Definite Integral
Addition
Local Maximum and Local Minimum of a
Definite Integral Function (Accumulation Function)
Ex
1: Area Under a Constant Function Using
Definite Integration
Ex
2: Area Under a Linear Function Using
Definite Integration
Ex
3: Area Under a Quadratic Function Using
Definite Integration
Ex
4: Area Under a Rational Function Using
Definite Integration
Ex
5: Area Under a Piece Wise Defined
Function Using Definite Integration
Ex: Definite Integral Involving a
Basic Linear Function
Ex: Definite Integral Involving a
Basic Rational Function
Ex: Definite Integral Involving a Rational
Function Requiring Simplifying
Ex: Definite Integration Application
- Cars Passing Through an Intersection
Ex: Definite Integration Involving a
Basic Trig Function (nonnegative)
Ex: Definite Integration Involving a
Basic Trig Function (above and below x-axis)
Determining
the value of a definite integral on the graphing calculator
Ex 1: The Second Fundamental Theorem
of Calculus
Ex 2: The Second Fundamental Theorem
of Calculus (Reverse Order)
Ex 3: The Second Fundamental Theorem
of Calculus
Ex 4: The Second Fundamental Theorem
of Calculus with Chain Rule
Ex 5: The Second Fundamental Theorem
of Calculus with Chain Rule
Applications of Definite Integration
Ex: Interpret the Meaning of Area Under a
Function
Ex
1: Application of Definite
Integration (Accumulated Sales)
Ex
2: Application of Definite
Integration (Distance)
Properties
of Definite Integrals and Average Value
Ex
1: Average Value of a Function
Ex
2: Average Value of a Trig Function
Point
of Equilibrium
Consumer
and Producer Surplus
Present and Future Value:
Part 1, Part 2
Area Bounded by Two Functions
Area Between to Graphs
Ex 1: Area Bounded by Two Functions
Ex 2: Area Bounded by Two Functions (2 Regions)
Ex 3: Area Bounded by Two Trig Functions
Integration by Substitution
Integration by Substitution:
Part 1, Part 2
Ex
1: Integration Using Substitution
Ex
2: Integration Using Substitution
Ex
3: Integration Using Substitution
Ex
4: Integration Using Substitution
Ex
5: Integration Using Substitution
Ex
6: Integration Using Substitution
Ex
7: Integration Using Substitution
Ex
8: Integration Using Substitution
Involving Trig Functions
Ex
9: Integration Using Substitution
Involving Trig Functions
Ex
1: Definite Integration Using
Substitution
Ex
2: Definite Integration Using
Substitution
Ex: Indefinite Integral Using
Substitution Involving a Square Root
Ex: Indefinite Integral Using
Substitution Involving a Rational Function I
Ex: Indefinite Integral Using
Substitution Involving a Rational Function II
Ex: Indefinite Integral Using
Substitution with Exponential and Sine
Ex: Definite Integration Using
Substitution Involving Sine
Ex: Definite Integration Using
Substitution Involving Exponential and Trig Functions
Ex: Indefinite Integral Involving
Arcsine with Substitution
Indefinite integral: (sin(x))^2- Power Reducing Substitution
Indefinite Integral: (cos(2x))^2 - Power Reducing Substitution
Integration by Parts
Integration
by Parts: Basics
Integration
by Parts
Integration
by Parts: More Examples
Ex
1: Integration by Parts
Ex
2: Integration by Parts
Ex
3: Integration by Parts
Ex
4: Integration by Parts
Ex
5: Integration by Parts (Trig)
Ex
6: Integration by Parts Twice
Ex: Integration by Parts Involving a
Radical and Natural Log
Ex: Integration by Parts Involving a
Trig and Linear Function (x*cos(4x))
Ex: Integration by Parts - Definite
Integral Involving a Quadratic and Natural Log Function
Ex: Integration by Parts Twice
Application
Ex: Integration by Parts Twice and
Solving
Numerical Integration
Trapezoidal Rule of Numerical Integration
Simpson’s Rule of Numerical Integration
Improper Integrals
Improper Integral
Ex 1: Improper Integrals
Ex 2: Improper Integrals
Ex 3: Improper Integrals
Ex 4: Improper Integrals and Area
Ex: Area Using Improper Integrals
Differential Equations and Applications of Integration
Introduction
to Differential Equations
Differential
Equations and Exponential Functions
Solving
a differential equation by separation of variables
Ex: Find the Particular Solution to a Basic
Differential Equation
Ex: Future Value of One Time Investment
Ex: Present Value of One Time Investment Given
Future Value
Ex
1: Future Value of Continuous Money Flow
Ex
2: Continuous Money Flow needed for a
Given Future Value
Ex: Present Value of Continuous Money Flow
Ex: Future and Present Value of Continuous Money
Flow
Ex: Present Value of Perpetual Money Flow
Ex: Point of Equilibrium
Ex: Consumer Surplus
Ex: Producer Surplus
More Applications of Integration
Volume
of Revolution - The Disk Method
Volume
of Revolution - The Washer Method about the x-axis
Volume
of Revolution - The Washer Method about the y-axis
Volume
of Revolution - The Washer Method NOT about the x or y axis
Volume
of Revolution - The Shell Method about the x-axis
Volume
of Revolution - The Shell Method about the y-axis
Volume
of Revolution - The Shell Method NOT about x or y axis
Volume
of Revolution - Comparing the Washer and Shell Method
Arc
Length – Part 1
Arc
Length – Part 2
Surface
Area of Revolution – Part 1
Surface
Area of Revolution – Part 2
More Integration Techniques
Trig Integrals Involving Powers of Sine and Cosine: Part 1, Part 2
Trig Integrals Involving Powers of Secant and Tangent: Part 1, Part2
Partial Fraction Decomposition: Part 1, Part 2
Integration Using Partial Fraction Decomposition: Part 1, Part 2
Integration Involving Trigonometric Substitution: Part 1, Part 2, Part 3, Part 4
Ex 1: Integration Using Trigonometric
Substitution
Ex 2: Integration Using Trigonometric
Substitution
Ex 3: Integration Using Trigonometric
Substitution
Ex 4: Integration Using Trigonometric
Substitution
Ex 5: Integration Using Trigonometric
Substitution
Ex 6: Integration Using Trigonometric
Substitution
Ex: Integration Using Trigonometric
Substitution and Completing the Square
Ex 1: Definite Integration Using
Trigonometric Substitution
Ex 2: Definite Integration Using
Trigonometric Substitution
Wallis’s
Formula to Integrate Powers of Sine and Cosine on [0, pi/2]
Improper
Integrals
Ex
1: Improper Integrals
Ex
2: Improper Integrals
Ex 3: Improper Integrals
Ex
4: Improper Integrals and Area
Ex: Area Using Improper Integrals
Infinite Series
Introduction
to Sequences
Arithmetic
Sequences
Geometric
Sequences
Sequences
on the TI84 Graphing Calculator
Limits
of a Sequence
The
Squeeze Theorem
Arithmetic
Series
Geometric
Series
Introduction
to Infinite Series
Infinite Series: The Nth Term Divergent Test
Infinite
Geometric Series
Sequences
and Series on the TI84
Graph
Partial Sums of an Infinite Series on the TI84
Telescoping
Series
The
Integral Test
Infinite Series: The Integral Test
The
p-series Test
Infinite Series: The p-Series Test
The
Direct Comparison Test
Infinite Series: The Direct Comparison Test
The
Limit Comparison Test
Infinite Series: The Limit Comparison Test (Divergent)
Infinite Series: The Limit Comparison and Direct Comparison
Tests
Infinite Series: The
Limit Comparison and Ratio Tests - Part 1
Infinite Series: The
Limit Comparison and Ratio Tests - Part 2
The
Root Test
Infinite Series: The
Root Test I
Infinite Series: The
Root Test II
The
Ratio Test
Infinite Series: The
Ratio Test I
Infinite Series: The
Ratio Test II
The
Alternating Series Test
Conditionally
and Absolutely Convergent Series
Infinite Series: The Alternating Series Test
Taylor
Polynomials
Taylor’s
Theorem with Remainder
Power Series: Part 1, Part 2
Representing a Function as a Geometric Power Series: Part 1, Part 2
Taylor
and Maclaurin Series
Using Power Series Tables – Part 1, Part 2
Differentiating
and Integrating Using Power Series
Parametric Equations
Introduction to Parametric
Equations
Graphing
Parametric Equations in the TI84
Converting
Parametric Equation to Rectangular Form
Ex 1: Write Parametric
Equations as a Cartesian Equation
Ex 2: Write Parametric
Equations as a Cartesian Equation
Ex 3: Write Parametric
Equations as a Cartesian Equation
Ex 4: Write Parametric
Equations as a Cartesian Equation
Ex: Parametric
Equations for an Ellipse in Cartesian Form
The
Derivative of Parametric Equations
Second Derivative of Parametric Equations: Part 1, Part 2
Arc
Length in Parametric Form
Surface
Area of Revolution in Parametric Form
Polar Coordinates and Equations
Introduction
to Parametric Equations
Graphing
Parametric Equations in the TI84
Converting
Parametric Equation to Rectangular Form
Ex 1: Write Parametric
Equations as a Cartesian Equation
Ex 2: Write Parametric
Equations as a Cartesian Equation
Ex 3: Write Parametric
Equations as a Cartesian Equation
Ex 4: Write Parametric
Equations as a Cartesian Equation
Ex: Parametric
Equations for an Ellipse in Cartesian Form
The
Derivative of Parametric Equations
Ex 1: Equation of a
Tangent Line to a Curve Given by Parametric Equations
Ex 2: Equation of a
Tangent Line to a Curve Given by Parametric Equations
Ex 3: Equation of a
Tangent Line to a Curve Given by Parametric Equations
Determine the Points
Where the Tangent Lines are Horizontal or Vertical Using Parametric Equations
Second Derivative of Parametric Equations: Part 1, Part 2
Ex: Determine the
First and Second Derivative Given Parametric Equations
First and Second
Derivative of Parametric Equations - Concavity
Arc
Length in Parametric Form
Ex 1: Determine the
Arc Length of a Curve Given by Parametric Equations
Ex 2: Determine the
Arc Length of a Curve Given by Parametric Equations
Find the Length of a
Loop of a Curve Given by Parametric Equations
Surface
Area of Revolution in Parametric Form
Ex 1: Surface Area of
Revolution in Parametric Form
Ex 2: Surface Area of
Revolution in Parametric Form
Graphing Polar Equations
Graph
Polar Equations I
Graph
Polar Equations II
Animation: Graph Polar Equations
Graph Conic Sections in Polar Form: Part 1, Part 2, Part 3
Conics
in Polar Form and Graphing a Parabola in Polar Form
Graphing
an Ellipse in Polar Form
Graphing a Hyperbola
in Polar Form
Area using Polar Coordinates: Part 1, Part 2, Part 3
Area between Polar Curves:
Part 1, Part 2
The
Slope of a Tangent Line to a Polar Curve
Horizontal
and Vertical Tangent Lines to a Polar Curve
Arc Length
of a Polar Curve
Surface
Area of Revolution of a Polar Curve
Vectors
Introduction
to Vectors
Vector
Operations
Unit
Vector
Find the Component
Form of a Vector from the Graph of a Vector
Ex: Find the Direction and Magnitude of a Vector
in Component Form
Find the Component
Form of a Vector Given Magnitude and Direction
Ex: Write a Vector as a Combination of Two
Vectors
Ex: Find the Net Force of Three Vectors and the
Opposite Force
Ex: Find the Coordinates of a Rotated Point Using
Vectors
Ex: Direction and Speed of a Plane in the Wind
Using Vectors
Applications of Vectors
Applications
of Vectors
Determining
the Angle Between Two Vectors
Proof
of the formula for the Angle Between Two Vectors
Vector
Projection
Proof
of the Vector Projection Formula
Vector
Applications: Force and Work
Vectors in Space
Plotting
Points in 3D
The
Equation of a Sphere
Vectors
in Space
Parallel
Vectors
Vector
Cross Products
An
Application of Cross Products: Torque
The
Triple Scalar Product: Volume of a
Parallelepiped
Parametric
Equations of Lines in 3D
The
Equation of a Plane in 3D Using Vectors
Graphing
a Plane in 3D
Determining
the Angle Between Two Planes
Determining
the Distance Between a Plane and a Point
Determining
the Distance Between a Line and a Point
Quadric, Surfaces, Cylindrical Coordinates and Spherical
Coordinates
Cylindrical
Surfaces
Introduction
to Quadric Surfaces
The
Ellipsoid
The
Hyperboloid of One Sheet
The
Hyperboloid of Two Sheets
The
Elliptical Cone
The
Elliptical Paraboloid
The
Hyperbolic Paraboloid
Surfaces
of Revolution
Cylindrical
Coordinates
Converting
Between Cylindrical and Rectangular Equations
Spherical
Coordinates
Converting
Between Spherical and Rectangular Equations
Vector Valued Functions
Introduction
to Vector Valued Functions
The
Domain of a Vector Valued Function
Determining
a Vector Valued Function from a Rectangular Equation
Determine
a Vector Valued Function from the Intersection of Two Surfaces
Limits
of Vector Valued Functions
The
Derivative of a Vector Valued Function
Determining
Where a Space Curve is Smooth from a Vector Valued Function
Indefinite Integration of Vector Valued
Functions
Indefinite
Integration of Vector Valued Functions with Initial Conditions
Definite Integration of Vector
Valued Functions
Properties
of the Derivatives of Vector Valued Functions
The
Derivative of the Cross Product of Two Vector Valued Functions
Determining
Velocity, Speed, and Acceleration Using a Vector Valued Function
Determining
the Unit Tangent Vector
Determining
the Unit Normal Vector
Proving
the Unit Normal Vector Formula
Determining
a Tangent Line of a Curve Defined by a Vector Valued Function
Determining
the Tangential and Normal Components of Acceleration
Determining
Arc Length of a Curve Defined by a Vector Valued Function
Determining
Curvature of a Curve Defined by a Vector Valued Function
Determining
the Binormal Vector
Functions of Several Variables
Introduction
to Functions of Two Variables
Level
Curves of Function of Two Variables
Limits
of Functions of Two Variables
First
Order Partial Derivatives
Second
Order Partial Derivatives
Differentials
of Functions of Two Variables
Applications
of Differentials of Functions of Several Variables
The
Chain Rule for Functions of Two Variables With One Independent Variable
The
Chain Rule for Functions of Two Variables With Two Independent Variable
Implicit
Differentiation of Functions in One Variable using Partial Derivatives
Partial
Implicit Differentiation
Directional
Derivatives
The
Gradient
Determining
a Unit Normal Vector to a Surface
Verifying
the Equation of a Tangent Plane to a Surface
Determining
the Equation of a Tangent Plane
Determining
the Relative Extrema of a Function of Two Variables
Absolute
Extrema of Functions of Two Variables
Applications
of Extrema of Functions of Two Variables I
Applications
of Extrema of Functions of Two Variables II
Applications
of Extrema of Functions of Two Variables III
Lagrange
Multipliers - Part 1
Lagrange
Multipliers - Part 2
Double Integrals
Integrating
Functions of Two Variables
Introduction
to Double Integrals and Volume
Evaluating
Double Integrals
Double
Integrals and Volume over a General Region - Part 1
Double
Integrals and Volume over a General Region - Part 2
Average
Value of a Function of Two Variables
Fubini's
Theorem
Setting
up a Double Integral Using Both Orders of Integration
Double
Integrals: Changing the Order of
Integration
Double
Integrals: Changing the Order of Integration - Example 1
Double
Integrals: Changing the Order of Integration - Example 2
Introduction
to Double Integrals in Polar Coordinates
Double
Integrals in Polar Coordinates - Example 1
Double
Integrals in Polar Coordinates - Example 2
Area
Using Double Integrals in Polar Coordinates - Example 1
Area
Using Double Integrals in Polar Coordinates - Example 2
Triple Integrals
Introduction
to Triple Integrals
Evaluating
Triple Integrals – Example
Triple
Integrals and Volume - Part 1
Triple
Integrals and Volume - Part 2
Triple
Integrals and Volume - Part 3
Application
of Triple Integrals: Mass
Changing
the Order of Triple Integrals
Triple Integrals
Using Cylindrical Coordinates
Triple
Integral and Volume Using Cylindrical Coordinates
Rewrite
Triple Integrals Using Cylindrical Coordinates
Introduction
to Triple Integrals Using Spherical Coordinates
Triple
Integrals and Volume using Spherical Coordinates
A
Change of Variables for a Double Integral:
Jacobian
Example
of a Change of Variables for a Double Integral:
Jacobian
A
Change of Variables for a Triple Integral:
Jacobian
Vector Calculus
Introduction
to Vector Fields
The
Divergence of a Vector Field
The
Curl of a Vector Field
Conservative
Vector Fields
Defining
a Smooth Parameterization of a Path
Line
Integrals in R^2
Line
Integrals in R^3
Line
Integral of Vector Fields
Line
Integrals in Differential Form
Determining
the Potential Function of a Conservative Vector Field
The
Fundamental Theorem of Line Integrals - Part 1
The
Fundamental Theorem of Line Integrals - Part 2
Fundamental
Theorem of Line Integrals - Closed Path/Curve
Green's
Theorem - Part 1
Green's
Theorem - Part 2
Determining
Area using Line Integrals
Flux
Form of Green's Theorem
Parameterized
Surfaces
Area of
a Parameterized Surface
Surface
Integral with Explicit Surface Part 1
Surface
Integral with Explicit Surface Part 2
Surface
Integrals with Parameterized Surface - Part 1
Surface
Integrals with Parameterized Surface - Part 2
Surface
Integral of a Vector Field - Part 1
Surface
Integral of a Vector Field - Part 2
Stoke's
Theorem - Part 1
Stoke's
Theorem - Part 2
The
Divergence Theorem - Part 1
The
Divergence Theorem - Part 2
Graphing Calculator
Determine
the value of the derivative function on the graphing calculator
Determining
the value of a definite integral on the graphing calculator
Sequences
on the TI84 Graphing Calculator
Sequences
and Series on the TI84
Graph
Partial Sums of an Infinite Series on the TI84
Graphing
Parametric Equations in the TI84
