**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).