1. The Fundamental Theorem of Calculus
AP Calculus BC
March 22, 2017
Mrs. Agnew

2. Essential Stuff Essential Question Essential Vocabulary
What does the Fundamental Theorem of Calculus say?
Essential Vocabulary
Fundamental Theorem of Calculus
Total Change Theorem
Evaluation Theorem

3. Calculus’s Theorem
The FTC establishes the connection between Differential and Integral Calculus.
Differential Calculus: the tangent line problem
Integral Calculus: the area problem
The FTC states that differentiation and integration have an inverse relationship.

4. The Theorem, Part 1
Assumptions:
Conclusion:

5. The Theorem, Part 1
If we first integrate and then differentiate, we get back the same function.
Examples
What if we differentiate then integrate?

6. Fundamental Theorem of Calculus
Suppose f is continuous on [a,b]… 1. 2.
Evaluation Theorem

7. The FTC Reformed
The integral of a rate of change is the total change.

8. Homework: 3/22/17 Guided Practice Homework Page 386 – 387 #12 – 19
Smith & Minton Worksheet
#6, 11, 13, 18, 29 – 33, 36, 40, 42, 48, 50, 61