1. Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
The Fundamental Theorem of Calculus is appropriately named because it establishes connection between the two branches of calculus: differential calculus and integral calculus.
DEFINITION
Example
A function is called an
antiderivative of if
Let:
Find the an antiderivative

2. Example: Example: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2
Example:
Evaluate the integral
Example:
Find the area under the curve from x-0 to x=1

3. Example: Example: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2
Example:
Evaluate the integral
Example:
Find the area under the curve from x-0 to

4. Example: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
THE FUNDAMENTAL THEOREM OF CALCULUS, PART 2
Example:
Evaluate the integral

5. Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
Define:
Example:
Example:

6. Example: Note: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1
Example:
Find the derivative of the function
Note:
Using Leibniz notation

7. Note: Example: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1
Note:
Using Leibniz notation
Example:
Find

8. Note: Example: Note: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1
Note:
Using Leibniz notation
Example:
Find
Note:

9. Note: Example: Note: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1
Note:
Using Leibniz notation
Example:
Find
Note:

10. Note: Note: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1
Note:
Using Leibniz notation
Note:

11. Note Note Sec 5.3: 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

12. TERM-102

13. TERM-102

14. TERM-092

15. TERM-082

16. TERM-082

17. TERM-082

18. TERM-091

19. TERM-093

20. TERM-091

31. Term-092

32. Term-082