AP Calculus November 29-30, 2016 Mrs. Agnew

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Presentation transcript:

AP Calculus November 29-30, 2016 Mrs. Agnew Antiderivatives AP Calculus November 29-30, 2016 Mrs. Agnew

Essential Stuff Essential Question Essential Vocabulary What is the antiderivative of a function? Essential Vocabulary General Antiderivative Particular Antiderivative Initial Condition

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.

Finding Antiderivatives Antidifferentiation is the process by which we “work backwards.” The antiderivative is the function whose derivative is the given function. Examples…

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: ∫

Antidifferentiation Formulas Function Antiderivative

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

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