 # 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 ?

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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 ?

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.

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

Examples

Integration Formula

Examples

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

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