Average Values

For the average value of a function: Change the lower bound (point A) and upper bound (point B) of the function to see its definite integral and average value.

For the average value of a discrete list: Input values to see how the average value of the list changes.

For the average y value of a discrete set of points: Change each x-value to see how the average y value
of the five points is affected.

Use the shift key to drag the window or Ctrl + '+' and Ctrl + '-' to zoom in and out.

Average y value-discrete set of points.ggb

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Average Value of a function.ggb

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Average value- discrete.ggb

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Why is the area of the definite integral equal to the area of the of rectangle?

What happens to the average value of the function if there is "negative" area (area beneath the x-axis) in the definite integral?

Describe three ways in which the average y value of a function is related to the average y value of a discrete set of points.


Objectives:
-Students will visualize the concept of average value of a continuous function and describe how it relates to area under the curve.
-Students will discover how the average value of a continuous function is related to average value of a discrete set of points.