4_9 - Section 4.9 Antiderivatives Instructor Ms Hoa...

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Unformatted text preview: Section 4.9: Antiderivatives Instructor: Ms. Hoa Nguyen ([email protected]) Definition The problem is to find a function F whose derivative is a known function f . If such a function F exists, it is called antiderivative of f . Definition : A function F is called an antiderivative of f on an interval I if F ( x ) = d dx F = f ( x ) for all x in I . Example : Given f ( x ) = x 2 , • 1. Find an antiderivative of f . • 2. Are there any other antiderivatives? If yes, then what is the most general antiderivative of f ? ( Hint : the Mean Value Theorem) • 3. Draw the graphs of a family of functions derived from the above general antiderivative. These graphs are vertical translates of one another. This makes sense, as each curve must have the same slope at any given value of x. 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....
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4_9 - Section 4.9 Antiderivatives Instructor Ms Hoa...

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