Mean Value Theorem for Integrals

Explain what the Mean Value Theorem for Integrals says using plain English (i.e., without using any mathematical notation).

Use the applet above to determine what you can say about the value of guaranteed by the Mean Value Theorem for Integrals if the function is linear.

Edit the applet below to find (another example of) a function f and an interval to show that your finding from the previous problem is not true in general. Experiment to see how close you can get to .