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

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

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

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

Sec 4.9: Antiderivatives Indefinite Integral Example Evaluate: 5

Sec 4.9: Antiderivatives F131

Sec 4.9: Antiderivatives F092

F101

Sec 4.9: Antiderivatives TABLE OF ANTIDIFFERENTIATION FORMULAS

Sec 4.9: Antiderivatives 10

Sec 4.9: Antiderivatives F141 11

Sec 4.9: Antiderivatives F141

Sec 4.9: Antiderivatives F132 13

Sec 4.9: Antiderivatives F101 14

Sec 4.9: Antiderivatives F132 15

Sec 4.9: Antiderivatives

Sec 4.9: Antiderivatives F151

Sec 4.9: Antiderivatives

Sec 4.9: Antiderivatives F143

Sec 4.9: Antiderivatives F143

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