Find the Average Value of a Function — Practice Questions

By Mark Ryan

Although differentiation helps you figure out a lot of things about a function, there’s one thing that differentiation cannot answer: What’s the function’s average height? To answer that, you need integration.

The following practice questions ask you to find average values using integration.

Practice questions

  1. What’s the average value of


  2. A car’s speed in feet per second is given by f(t) = t1.7 – 6t + 80. What’s its average speed from t = 5 seconds to t = 15 seconds? What’s that in miles per hour?

Answers and explanations

  1. The average value is 0.03.


    Do this with a u-substitution.


  2. The car’s average speed is about 72.62 feet per second, or 49.51 miles per hour.