1. The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus and integral calculus. THE FUNDAMENTAL THEOREM OF CALCULUS Let: Find the an antiderivative Example A function is called an antiderivative of if DEFINITION

2. Example: THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 THE FUNDAMENTAL THEOREM OF CALCULUS Evaluate the integral Example: Find the area under the curve from x-0 to x=1

3. Example: THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 THE FUNDAMENTAL THEOREM OF CALCULUS Evaluate the integral Example: Find the area under the curve from x-0 to

4. Example: THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2 THE FUNDAMENTAL THEOREM OF CALCULUS Evaluate the integral

5. Define: Example: THE FUNDAMENTAL THEOREM OF CALCULUS Example:

6. THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 THE FUNDAMENTAL THEOREM OF CALCULUS Find the derivative of the function Note: Using Leibniz notation

7. Example: THE FUNDAMENTAL THEOREM OF CALCULUS Find THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note: Using Leibniz notation

8. THE FUNDAMENTAL THEOREM OF CALCULUS THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note: Using Leibniz notation Example: Find Note:

9. THE FUNDAMENTAL THEOREM OF CALCULUS Note:

10. Note THE FUNDAMENTAL THEOREM OF CALCULUS which says that if f is integrated and then the result is differentiated, we arrive back at the original function Note This version says that if we take a function, first differentiate it, and then integrate the result, we arrive back at the original function

11. Total Area Example Evaluate:

12. Total Area

13. Example Find the area of the region between the x-axis and the graph of Example Find the area of the region between the x-axis and the graph of What is the difference between these two examples

14. TERM-102

16. TERM-092

17. TERM-082

20. TERM-091

21. TERM-093

22. TERM-091

31. Term-092

32. Term-082