1. SECTION 4-4 A Second Fundamental Theorem of Calculus

2. 1) Find by working from inside out: - First integrate - Then differentiate constant Recall: Derivatives and Integrals undo each other. They are inverses

3. Second Fundamental Theorem of Calculus If f(x) is continuous on [a,b], then the derivative of is

4. What if both limits have variables?

5. 2) Find 3) Find

6. 4) Find 5) Find

7. What if the upper limit is a function other than x? 6) Find ifthen

8. 7) Find 8) Find

9. 9) Find ifthen What if both limits have variables?

10. 10) Find 11) Find

11. Net Change Theorem The definite integral of the rate of change of a quantity F’(x) gives the total, or net change, in that quantity on the interval [a, b].

12. 12) Find the displacement (net change) of a particle moving along a line so that its velocity is feet per second. a) What is the displacement on the time interval [1, 5]

13. 12) cont b) What is the total distance traveled by the particle [1, 5]

14. Assignment: Page 295 # 75-92, 97, 98 and 99