From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Definite Integrals

Definite Integrals

Averages with Functions Exercises

Example 1

Let f (x) = 3x. Find a constant m such that

Example 2

Let f (x) = x. Find a constant m such that

Example 3

Find the average value of the function on the specified interval. Check and make sure your answer has the sign you would expect.

  •  f (x) = x on [-10, 0]

Example 4

Find the average value of the function on the specified interval. Check and make sure your answer has the sign you would expect.

  •  on [-2, 2]

Example 5

Find the average value of the function on the specified interval. Check and make sure your answer has the sign you would expect.

  • f (x) = sin x on [-π, π]

Example 6

Find the average value of the function on the specified interval. Check and make sure your answer has the sign you would expect.

  • f (x) = 3x + 2 on [1, 4]

Example 7

Find the average value of the function on the specified interval. Check and make sure your answer has the sign you would expect.

  •  f (x) = -2x – 1 on [-4, 2]
Advertisement