Chapter 5 Videos
Section 5.1
Lesson 1: An Intro to Area Estimates and Riemann Sums
Another Example of Computing a Basic Riemann Sum
Example of Computing a Negative Riemann Sum
Examples: Upper, Lower, Left-hand and Right-hand Sums
Section 5.2
Lesson 1: The Basics of Sigma Notation
Lesson 2: Using Sigma Notation for Large Sums
Lesson 3: Sigma Notation with Riemann Sums (This is tough, and it’s a long video at 30 minutes but I really try to go through every single single on this to help you understand. Be mentally prepared to take this all in, it will likely take you longer than 30 minutes to truly absorb.)
Extra Example 1: Calculating a Limit as n -> infinity for a Riemann Sum
Extra Example 2: Calculating a Limit as n -> infinity for a Riemann Sum
Section 5.3
Lesson 1: Understanding the Basics of Definite Integrals (from a theoretical perspective)
Lesson 2: Using Area Formulas to Calculate Definite Integrals
Lesson 3: Calculating the Average Value of Functions
Section 5.4
Lesson 1: The Fundamental Theorem of Calculus, part 1!
Examples of the Fundamental Theorem of Calculus part 1, integrating then differentiating vs differentiating directly
Examples of the Fundamental Theorem of Calculus part 1 differentiating directly
Step-by-Step Example of the Fundamental Theorem of Calc part 1: using the product rule?
Lesson 2: The Fundamental Theorem of Calculus, part 2!!
Examples of Evaluating Definite Integrals - Basic Examples
Examples of Evaluating Definite Integrals - Tricky Trig Examples
Examples of Evaluating Definite Integrals - Tricky Non-Trig Examples
Lesson 3: An Example Showing How all the Formulas Relate
Summary: How the Heck Do You Know Which Technique to Use with Which Type of Integral?
Section 5.5
Lesson 1: An Overview of the Substitution Method - A Long but Complete Guide
Lesson 2: Using the Substitution Method with New Trig Integrals
Basic Examples of the Substitution Method
Examples of the Substitution Method where Some Manipulation is Needed
Difficult Examples of the Substitution Method where Significant Creativity is Needed
Section 5.6
Lesson 1: Two Ways of Evaluating Definite Integrals using the Substitution Method
Examples: Substitution and Definite Integrals
Step-by-Step Example: Substitution and Definite Integrals where Simplifying the Final Answer is Tricky
Step-by-Step Example: Substitution and Definite Integrals with Tricky Trig
Lesson 2: Symmetric Functions and Definite Integrals