Integration.

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Presentation transcript:

Integration

The Reverse of the Derivative is the Antiderivative Also called the Integral (symbol ∫ ) Why would you need it? - If you knew velocity (s’) but wanted to get position (s) - If you know the growth rate (p’) and want to get the population (p)

Definition A function (F) is called an antiderivative of f if F’(x) = f(x) for all x on an interval Example: f(x) = x2 F(x) =

From the previous example, we notice that F(x) = x2 could have many antidervivatives that work

General Form If F is an antiderivative of f, then the most general form of the antiderivative is F(x) + C where C is a constant

Common Antiderivatives

Example