1. MAT 1235 Calculus II 4.3 Part I The Fundamental Theorem of Calculus http://myhome.spu.edu/lauw

2. Friendly Competition....

3. Next WebAssign HW 4.3 I

4. Preview Fundamental theorem of Calculus Part I Connection between Differential and Integral Calculus (What is the derivative of an integral?) Important for understanding of advanced mathematics

5. Consider the function…

6. Fundamental Theorem of Calculus Part I

7. Why is this important?

8. Major Themes in Calculus II

9. Definite integral - accumulation of physical quantities (energy, charges, pressure…) We want to know how “fast” is the accumulation.

10. How do I know this is true?

11. Fundamental Theorem of Calculus Part I Proof: (Too Long) Verify with example:

12. Fundamental Theorem of Calculus Part I Proof: (Too Long) Verify with example:

13. Fundamental Theorem of Calculus Part I

14. Remarks constant same variable

15. Example 1 (a) (b)

16. Example 2

17. Example 3

18. Cannot apply the theorem……..

19. Example 3 This reminds us of……..?

20. Recall: Chain Rule

21. Example 3

22. Example 4

23. Cannot apply the theorem…….. not x not constant

24. Example 4