Ch 4 - Integration
Chapter 4 PDF Resource
| calculus_chapter_4.pdf |
Lecture Notes & Videos
Section 4-1
Antiderivatives & Indefinite Integration
-----VIDEO: Brief Introduction to the Antiderivative and Indefinite Integration (Part 1 of 2)
-----VIDEO: Integration using the Power Rule (Part 2 of 2)
-----VIDEO: Integrating Basic Trig Functions
Section 4-2
Area Using Left & Right Endpoints
-----VIDEO: Finding the Area Under a Curve using Left & Right Endpoints (A Prelude to a Riemann Sum and the Definite Integral)
-----VIDEO: An Introduction to Summation (Sigma) Notation
-----VIDEO: Summation (Sigma) Notation on the TI-84
Section 4-3
Riemann Sums & Definite Integrals
-----VIDEO: A Brief Introduction to a Riemann Sum
-----VIDEO: A Brief Introduction to the Definite Integral (Part 1)
-----VIDEO: 5 Examples that Connect the Definite Integral to the Area Under the Curve (Part 2)
Section 4-4 (Day 1)
The Fundamental Theorem of Calculus
-----VIDEO: Fundamental Theorem of Calculus (FTC)
Section 4-4 (Day 2)
Mean Value Theorem for Integrals
-----VIDEO: Mean Value Thm for Integrals & Average Value
-----VIDEO: 3 Examples Dealing with Definite Integrals
Riemann Sums from a Table of Values
-----VIDEO: AP Calculus AB: A Riemann Sum from a Table of Values
Riemann Sum Handout
Section 4-5 (Day 1)
Integration by Substitution
-----VIDEO: Integration: U-Substitution Method
Section 4-5 (Day 2)
Indefinite Integrals with Trig & Definite Integrals
-----VIDEO: Indefinite Integrals: U-Substitution Method with Trig Functions
Section 4-6
Trapezoidal Rule and Simpson's Rule
More Examples of Trapezoidal Rule, Riemann Sums, and Simpson's Rule
The Derivative of an Integral
Total Distance Traveled & Displacement Notes
Total Distance Traveled & Displacement Typed Summary
Antiderivatives & Indefinite Integration
-----VIDEO: Brief Introduction to the Antiderivative and Indefinite Integration (Part 1 of 2)
-----VIDEO: Integration using the Power Rule (Part 2 of 2)
-----VIDEO: Integrating Basic Trig Functions
Section 4-2
Area Using Left & Right Endpoints
-----VIDEO: Finding the Area Under a Curve using Left & Right Endpoints (A Prelude to a Riemann Sum and the Definite Integral)
-----VIDEO: An Introduction to Summation (Sigma) Notation
-----VIDEO: Summation (Sigma) Notation on the TI-84
Section 4-3
Riemann Sums & Definite Integrals
-----VIDEO: A Brief Introduction to a Riemann Sum
-----VIDEO: A Brief Introduction to the Definite Integral (Part 1)
-----VIDEO: 5 Examples that Connect the Definite Integral to the Area Under the Curve (Part 2)
Section 4-4 (Day 1)
The Fundamental Theorem of Calculus
-----VIDEO: Fundamental Theorem of Calculus (FTC)
Section 4-4 (Day 2)
Mean Value Theorem for Integrals
-----VIDEO: Mean Value Thm for Integrals & Average Value
-----VIDEO: 3 Examples Dealing with Definite Integrals
Riemann Sums from a Table of Values
-----VIDEO: AP Calculus AB: A Riemann Sum from a Table of Values
Riemann Sum Handout
Section 4-5 (Day 1)
Integration by Substitution
-----VIDEO: Integration: U-Substitution Method
Section 4-5 (Day 2)
Indefinite Integrals with Trig & Definite Integrals
-----VIDEO: Indefinite Integrals: U-Substitution Method with Trig Functions
Section 4-6
Trapezoidal Rule and Simpson's Rule
More Examples of Trapezoidal Rule, Riemann Sums, and Simpson's Rule
The Derivative of an Integral
Total Distance Traveled & Displacement Notes
Total Distance Traveled & Displacement Typed Summary
Worksheets
Cumulative Review WS (Chapters 1-3)
Riemann Sum WS w/ Unequal Subintervals
Open Ended AP Questions WS #5
Riemann Sums WS
Sections 4-1 to 4-4 Review WS
Sections 4-1 to 4-4 Review WS KEY
Sections 4-1 to 4-4 Review WS #2
Sections 4-1 to 4-4 Review WS #2 KEY
Miscellaneous Cumulative Review Thru Section 4-4 WS
Miscellaneous Cumulative Review Thru Section 4-4 WS KEY
Related Rates & Optimization Review WS
Open Ended AP Questions WS #6
Simpson's Rule & Review of Trapezoidal Rule/Riemann Sum WS
Derivatives & Integrals Review WS
Distance Traveled vs Displacement WS
The Derivative of an Integral WS
1st Derivative & 2nd Derivative Function Analysis AP Practice
Integration Review WS #1
Chapter 4 Review WS
Chapter 4 Review WS KEY
Riemann Sum WS w/ Unequal Subintervals
Open Ended AP Questions WS #5
Riemann Sums WS
Sections 4-1 to 4-4 Review WS
Sections 4-1 to 4-4 Review WS KEY
Sections 4-1 to 4-4 Review WS #2
Sections 4-1 to 4-4 Review WS #2 KEY
Miscellaneous Cumulative Review Thru Section 4-4 WS
Miscellaneous Cumulative Review Thru Section 4-4 WS KEY
Related Rates & Optimization Review WS
Open Ended AP Questions WS #6
Simpson's Rule & Review of Trapezoidal Rule/Riemann Sum WS
Derivatives & Integrals Review WS
Distance Traveled vs Displacement WS
The Derivative of an Integral WS
1st Derivative & 2nd Derivative Function Analysis AP Practice
Integration Review WS #1
Chapter 4 Review WS
Chapter 4 Review WS KEY
Study Guides (Used Prior to 2021-22)
Interactive Animations
Calculus is the study of change. The ability to change a parameter and immediately see the result can demonstrate that change and how things are related during that change. Many of these concepts are much easier to explain if that change, the motion, can be visually demonstrated in class. Therefore, this is a perfect place for the use of computer animations.
All animations were created using the GeoGebra dynamic mathematics software application located on GeoGebra's website.
All animations were created using the GeoGebra dynamic mathematics software application located on GeoGebra's website.
Please be patient! It takes awhile for these to load.
Widen the browser, if necessary, to see the entire animation.
Widen the browser, if necessary, to see the entire animation.
Riemann, Trapezoidal, & Simpson's Approximation Comparison
This dynamic illustration demonstrates various area approximations using a Riemann Sum, Trapezoidal Rule, and Simpson's Rule.
In this version, the user can enter the function, a, and b (where a < b). The user can choose n as any even number between 2 and 12 (even because of Simpson's Rule).
In this version, the user can enter the function, a, and b (where a < b). The user can choose n as any even number between 2 and 12 (even because of Simpson's Rule).
