2. Antiderivatives Definition A function F(x) is called an antiderivative of f(x) if F ′(x) = f (x). Examples: What’s the antiderivative of f(x) = 1/x ? What’s the antiderivative of g(x) = 2x ? What’s the antiderivative of h(x) = 4 ?

3. Antiderivatives Theorem If F(x) is an antiderivative of f (x), then the most general antiderivative of f(x) is the family of functions given by F(x) + c, where c is an arbitrary constant. Example: Determine the most general antiderivative of the following functions.

4. Notations for Antiderivatives Definition The operation of finding the antiderivatives of a function f(x) is called antidifferentiation (or Integration) and is denoted by the integral sign Variable of integration Constant of integration integrand Integral sign Antiderivative

5. Examples

6. Integration Formula

8. Examples

9. 1) Determine f (x) if 2) Find the cost function for each marginal cost function. C’(x) = 5x – 1/x ; 10 units cost $94.20