1. The Fundamental Theorem of Calculus (FTC)
Section 4.4 – Part 2
The Fundamental Theorem of Calculus
(FTC)

2. FTC Part 2 Definite Integral as a number
To understand FTC part 2, we need to think of the integral as a function.
Definite Integral as a number
Definite Integral as a Function
F is a function of x
Constant
f is a function of x
f is a function of t
Constant
Constant

3. Ex: Evaluate the following function at

4. In the previous example, the derivative of F is the original integrand with only the variable changed. This brings us to FTC Part 2.

5. The second Fundamental Theorem of Calculus
If f is continuous on an open interval containing a, then, for every x in the interval,

6. Ex: Evaluate

7. Ex: Find the derivative of

8. Notes Break! Work on the following problems from your book:
p. 294 – 295 #66, 69 – 89 EOO

9. Distance VS Displacement
Distance: total amount traveled
Displacement: distance from starting point

10. **Remember: The derivative of the position function is the velocity function. The antiderivative of the velocity function is the position function.

11. Displacement:
Distance:

14. Homework Finish problems from p. 294 – 295 #66, 69 – 89 EOO