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Variable Limits of Integration and the Fundamental Theorem of Calculus

# Variable Limits of Integration and the Fundamental Theorem of Calculus

Unit 7: Applications of Integration

Lesson 3 of 14

Lesson 3 of 14

## Objective: SWBAT compute integrals with functions as limits of integration. SWBAT apply the Fundamental Theorem of Calculus in differentiating integrals with variable limits of integration.

## Big Idea: An integral with a variable limit of integration equals another function. So what is the derivative of such an integral? Let’s investigate…

Subject(s):

Math, Fundamental Theorem of Calculus, Precalculus and Calculus, Integrals, area (Integrals), AP Calculus AB, integration, calculus, AP Calculus, calculus ab

*60 minutes*

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- 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

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- 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)

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