## Lesson Plan, Areas Between Curves - dx or dy?, Investigation.docx - Section 4: Investigation

*Lesson Plan, Areas Between Curves - dx or dy?, Investigation.docx*

# Areas Between Curves - dx or dy?

Lesson 2 of 14

## Objective: SWBAT compute the area between two curves with respect to x and with y.

## Big Idea: For some regions, integrating with respect to x is more complicated. Integrating with respect to y can help.

*60 minutes*

Google Form - Submit answers online, AP As We Go #78,83,88

https://docs.google.com/spreadsheet/ccc?key=0AlOW3b0XTlhSdDBTQjdwWkN1UURMQjgzSmttbUNnLXc&usp=sharing

*expand content*

As I look back on these lessons, I feel like it most important to not let students get by without drawing the rectangles and writing out explicitly "X-x" or "Y-y"

No shortcuts is what I mean. If all that matters is the Integral setup, who cares if you are subtracting a negative or what have you. Many of our students reach this class with a great mental ability to do math, but are now reaching the point where their bad habits of not showing work are catching up to them. Tell them that their focus must be on the setup, not simplifying. If you do this, then volumes of solids of revolution will go more smoothly.

| one year ago | Reply

- 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: Easy as ABC - Areas Between Curves
- LESSON 2: Areas Between Curves - dx or dy?
- LESSON 3: Variable Limits of Integration and the Fundamental Theorem of Calculus
- LESSON 4: Catch-up Day - ABC and FTC
- LESSON 5: Volumes of Solids of Revolution (part 1 of 4)
- LESSON 6: Volumes of Solids of Revolution (part 2 of 4)
- LESSON 7: Volumes of Solids of Revolution (part 3 of 4)
- LESSON 8: Volumes of Solids of Revolution (part 4 of 4)
- LESSON 9: Volumes of Cross-Sectional Solids (part 1 of 4)
- LESSON 10: Volumes of Cross-Sectional Solids (part 2 of 4)
- LESSON 11: Volumes of Cross-Sectional Solids (part 3 of 4)
- LESSON 12: Volumes of Cross-Sectional Solids (part 4 of 4)
- LESSON 13: Applications and Problem Solving with Volumes of Solids (part 1 of 2)
- LESSON 14: Applications and Problem Solving with Volumes of Solids (part 2 of 2)