In this tutorial we are going to talk about finding the average value of a function over an interval. This computation requires using the definite integral. The exact computation is the definite integral divided by the width of the interval. This calculates the average height of a rectangle which would cover the exact area as under the curve, which is the same as the average value of a function. So, first, we are going to introduce the formula for calculating the average value of a function. Then we will see the origin of that formula and at the end we will do several examples concerning this topic.
I recommend that
you start by sketching the function!
Draw in the height
you think looks approximately correct for the average value.
At the end, check
your result with the height of your estimate!
If the problem
asks for a value
simply set these equal and solve for
Average Value of a Function
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.