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Section 15.1 - Antiderivatives

Section 15.1 - Antiderivatives. 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 ?.

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Section 15.1 - Antiderivatives

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  1. Section 15.1 - Antiderivatives

  2. Antiderivatives Definition A function F(x)is called an antiderivativeof f(x) if F ′(x) = f (x). Examples: What’s the antiderivativeof 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 Antiderivative Constant of integration Variable of integration Integral sign integrand

  5. Examples

  6. Integration Formula

  7. Integration Formula

  8. Examples

  9. 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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