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

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

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.

The Theorem, Part 1 Assumptions: Conclusion:

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

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

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

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