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# Cookies and Pi

Lesson 13 of 17

## Objective: SWBAT to apply the Fundamental Theorem of Calculus (FTC) to model and solve problems using integration.

## Big Idea: Everyone loves cookies, even calculus students. Students apply their knowledge of integration to divide a special cookie fairly.

*120 minutes*

#### Closure + Homework

*5 min*

**Closure Activity: **Explain to your neighbor how we used the Fundamental Theorem of Calculus today in class. Be specific about each use of the two parts of the FTC.

I want my students to understand the two parts of the FTC informally:

1) Derivatives and integrals “undo” each other

2) Definite integrals can be evaluated by computing the difference between the integrated function evaluated at the upper and lower limits of integration.

Our work with variable limits of integration, including on the warm-up, graphically with the Trace Area Under Curve v1 applet, and with the Cookies and Pi applet, rely heavily on part 2 of the FTC but obviously we cannot exclude the relevance of part #1 either.

**Tonight’s Homework:**

F - 1988 #40, 1993 #34,

I - By Hand, evaluate RRAM_{4} for on the interval .

V - TEXTBOOK – read examples, solve problems evaluating definite integrals with variable upper limits of integration given graphs.

E - Set 6: 1969 #41, 1973 #42, 1985 #42, 1988 #39, 1993 #12,41, 2003 #77

*expand content*

- UNIT 1: Back to School
- UNIT 2: Limits and Derivatives
- UNIT 3: Formalizing Derivatives and Techniques for Differentiation
- UNIT 4: Applications of Differentiation, Part 1
- UNIT 5: Applications of Differentiation, Part 2
- UNIT 6: The Integral
- UNIT 7: Applications of Integration
- UNIT 8: Differential Equations
- UNIT 9: Full Course Review via Motion
- UNIT 10: The Final Stretch - Preparing for the AP Exam

- LESSON 1: Limits and l'Hospital
- LESSON 2: Know Your Limits
- LESSON 3: Local Linearization, 1st and 2nd Derivative Tests, and Computing Derivatives
- LESSON 4: Derivatives Algebraically and Graphically
- LESSON 5: The Calculus of Motion
- LESSON 6: Motion - Velocity on Intervals
- LESSON 7: Motion - Distance vs Displacement
- LESSON 8: Motion - With Multiple Derivatives
- LESSON 9: Motion and Optimization
- LESSON 10: Calculus and My Car's Dashboard
- LESSON 11: Rockin' Related Rates
- LESSON 12: Meet My Friend Riemann
- LESSON 13: Cookies and Pi
- LESSON 14: Accumulate This!
- LESSON 15: Wait, the Interval Width Varies?
- LESSON 16: Integrating Areas to Get Volumes
- LESSON 17: More Areas and Volumes