1. Sec 4.9: Antiderivatives DEFINITION Example A function is called an
antiderivative of if
Let:
Find the an antiderivative
Can we find another one??
Example
Example
Let:
Find an antiderivative
Let:
Find an antiderivative
Example
Let:
Find an antiderivative

2. Sec 4.9: Antiderivatives Example Let: The most general
Thus the most general antiderivative of ƒ on I is a family of functions

3. Sec 4.9: Antiderivatives Example Example Example Let: The most general
Find f(x)
That satisfies
Let:
Find antiderivative
That satisfies
Solution:
Solution:

4. Sec 4.9: Antiderivatives TABLE OF ANTIDIFFERENTIATION FORMULAS Example
The most general antiderivative

5. Sec 4.9: Antiderivatives
Indefinite Integral
Example
Evaluate: 5

6. Sec 4.9: Antiderivatives
F131

7. Sec 4.9: Antiderivatives
F092

8. F101

9. Sec 4.9: Antiderivatives
TABLE OF ANTIDIFFERENTIATION FORMULAS

10. Sec 4.9: Antiderivatives 10

11. Sec 4.9: Antiderivatives
F141 11

12. Sec 4.9: Antiderivatives
F141

13. Sec 4.9: Antiderivatives
F132 13

14. Sec 4.9: Antiderivatives
F101 14

15. Sec 4.9: Antiderivatives
F132 15

16. Sec 4.9: Antiderivatives

17. Sec 4.9: Antiderivatives
F151

18. Sec 4.9: Antiderivatives

19. Sec 4.9: Antiderivatives
F143

21. Sec 4.9: Antiderivatives
F143

22. Sec 4.9: Antiderivatives Example
Thus the most general antiderivative of ƒ on I is a family of functions
Let:
The most general
antiderivative
whose graphs are vertical translations of one another.
Example
Let:
Find antiderivative
That satisfies