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AP Calculus November 29-30, 2016 Mrs. Agnew
Antiderivatives AP Calculus November 29-30, 2016 Mrs. Agnew
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Essential Stuff Essential Question Essential Vocabulary
What is the antiderivative of a function? Essential Vocabulary General Antiderivative Particular Antiderivative Initial Condition
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What Are Antiderivatives?
Assume we know a function for the velocity of an object. What if we wanted to know the object’s position? A function F is the antiderivative of f (x) if F’(x) = f(x) for all x over a given interval.
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Finding Antiderivatives
Antidifferentiation is the process by which we “work backwards.” The antiderivative is the function whose derivative is the given function. Examples…
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General Antiderivative
The general antiderivative of a function is F(x) + C, where C is an arbitrary constant. When finding the general antiderivative, you must add the constant C to the end of the antiderivative. Symbol for an Antiderivative: ∫
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Antidifferentiation Formulas
Function Antiderivative
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Particular Antiderivatives
General antiderivatives have the “ + C” If given a point on F (an initial condition), then we can find the value of C… the particular antiderivative. Guided Practice
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Homework: 11/29-30/16 Page 255 – 258 #19, 23, 27, 29, 35, 37, 40, 41, 43, 44, 59, 60, 62, 65, 70, 71, 73, 77, 84
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