1. The Fundamental Theorems of Calculus Lesson 5.4

2. First Fundamental Theorem of Calculus Given f is  continuous on interval [a, b]  F is any function that satisfies F’(x) = f(x) Then

3. First Fundamental Theorem of Calculus The definite integral can be computed by  finding an antiderivative F on interval [a,b]  evaluating at limits a and b and subtracting Try

4. Area Under a Curve Consider Area =

5. Area Under a Curve Find the area under the following function on the interval [1, 4]

6. Second Fundamental Theorem of Calculus Often useful to think of the following form We can consider this to be a function in terms of x View QuickTime Movie View QuickTime Movie

7. Second Fundamental Theorem of Calculus Suppose we are given G(x) What is G’(x)?

8. Second Fundamental Theorem of Calculus Note that Then What about ? Since this is a constant …

9. Second Fundamental Theorem of Calculus Try this

10. Assignment Lesson 5.4 Page 327 Exercises 1 – 49 odd