2311lectureoutline4.9

# 2311lectureoutline4.9 - Here’s are a few examples Let f(x...

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MAC2311, Calculus I 4.9 Antiderivatives Definition: A function F is called an antiderivative of f on an interval I if F’(x) = f(x) for all x in I . Theorem: If F is an antiderivative of f on an interval I , then the most general antiderivative of f on I is F(x) + C where C is an arbitrary constant. In general, if you are looking for the antiderivative of a function, you are really asking, “What function is this the derivative for?”
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Unformatted text preview: Here’s are a few examples: Let f(x) = cos(x). Since cos(x) is the derivative of the sin(x), then F(x) = sin(x) + C Let f(x) = 2x , so F(x) = x 2 + C Take a look at the handout with all of the derivative formulas to see the “antiderivative” formulas. Try exercises 4, 10, 14, 26, 30, 32, 38 on page 345 in your text....
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