9.1.1 Antidifferentiation

Question 1

Antidifferentiation

Answer 1

• 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).

Question 2

note

Answer 2

• 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.

Question 3

Find an antiderivative for

f (x) = 0.

Answer 3

F(x)=π

Question 4

Find a function whose derivative is 1.

Answer 4

x

Question 5

Find an antiderivative of the function

f (x) = 7e x.

Answer 5

7e^ x

Question 6

Find an antiderivative of the function

f (x) = x^ 2.

Answer 6

1/3x^3

Question 7

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)?

Answer 7

F (x) + 5

Question 8

Find an antiderivative of the function

f (x) = sec2 2x.

Answer 8

1/2tan2x