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What is the integral, and how is it used to solve problems?
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Student Learning Map
- Topic:Integrals
- Subject(s):Math
- Days:25
- Grade(s):11, 12
Key Learning:
To understand that integration is used to find areas and volumes, and to evaluate integrals using approximation methods and the Fundamental Theorem of Calculus.
Unit Essential Question(s):
Concept: Fundamental Theorem of Calculus, and Definite and Indefinite Integrals Lesson Essential Question(s):How can the area under a curve be estimated using the rectangular approximation methods and the Trapezoidal Method? (A)Lesson Essential Question(s):What is the Fundamental theorem of calculus and what makes it so important? (A)What is the Fundamental theorem of calculus and what makes it so important? (ET)How is the Fundamental Theorem of Calculus used to calculate the definite or indefinite integral of a functions? (A)Lesson Essential Question(s):How are antiderivatives used to find slope fields? (A)How are functions identified from their slope field? (A)How and why are some integrals evaluated by using substitution of variables? (A)How and why are some integrals evaluated by using substitution of variables? (ET)How and why are some integrals evaluated by using integration by parts? (A)How and why are some integrals evaluated by using integration by parts? (ET)
Additional Info:
Calculus textbook Graphing Calculator TI-Presenter Ancillary material
Resources:
Acquisition Lesson(s):
1. How can the area under a curve be estimated using the rectangular approximation methods and the Trapezoidal Method?2. What is the Fundamental theorem of calculus and what makes it so important?3. How are antiderivatives used to find slope fields?4. How is the Fundamental Theorem of Calculus used to calculate the definite or indefinite integral of a functions?5. How are functions identified from their slope field?6. How and why are some integrals evaluated by using substitution of variables?7. How and why are some integrals evaluated by using integration by parts?Extended Thinking Lesson(s):
1. What is the Fundamental theorem of calculus and what makes it so important?2. How and why are some integrals evaluated by using substitution of variables?3. How and why are some integrals evaluated by using integration by parts?