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AP Calculus AB: 9.1.1 Antidifferentiation

Mathematics8 CardsCreated 3 months ago

This content provides an overview of antidifferentiation—the process of finding a function whose derivative is a given function. It introduces the concept of antiderivatives, outlines how to reverse common derivative rules, and includes simple examples to illustrate the idea.

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Antidifferentiation

  • If you want to undo the derivative, try using the derivative formulas in reverse.

  • Antidifferentiation is a process or operation that reverses differentiation.

  • Given two functions, f and F, F is an antiderivative of f if F (x) = f(x).

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Key Terms

Term
Definition

Antidifferentiation

  • If you want to undo the derivative, try using the derivative formulas in reverse.

  • Antidifferentiation is a process or operat...

note

  • Suppose you are given the derivative of a function. How could you determine what the original function was?

  • A good start wou...

Find an antiderivative for

f (x) = 0.

F(x)=π

Find a function whose derivative is 1.

x

Find an antiderivative of the function

f (x) = 7e x.

7e^ x

Find an antiderivative of the function

f (x) = x^ 2.

1/3x^3

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AP Calculus AB: 9.1.1 Antidifferentiation
TermDefinition

Antidifferentiation

  • If you want to undo the derivative, try using the derivative formulas in reverse.

  • Antidifferentiation is a process or operation that reverses differentiation.

  • Given two functions, f and F, F is an antiderivative of f if F (x) = f(x).

note

  • Suppose you are given the derivative of a function. How could you determine what the original function was?

  • A good start would be to think about the different
    differentiation formulas in reverse. For example, since the power rule for derivatives requires you to subtract one from the exponent, perhaps you should add one when trying to undo the derivative.

  • The equation that you would have had before you took the derivative is called an antiderivative.

  • There is another way to think of it. An antiderivative of a function, f, is another function, F, whose derivative, F , is equal to the first function, f.

  • You might think of an antiderivative as the function you had before you took the derivative. However, you do not always have to take a derivative to find an antiderivative.

  • The process of finding an antiderivative is called
    antidifferentiation.

Find an antiderivative for

f (x) = 0.

F(x)=π

Find a function whose derivative is 1.

x

Find an antiderivative of the function

f (x) = 7e x.

7e^ x

Find an antiderivative of the function

f (x) = x^ 2.

1/3x^3

Suppose you are told that an antiderivative of the function f (x) is F (x). Which of the following is also an antiderivative of f (x)?

F (x) + 5

Find an antiderivative of the function

f (x) = sec2 2x.

1/2tan2x