This file is part of a distribution of the Calculus Applets website (http://www.calculusapplets.com) (v1.1) which has been reformatted for the needs of this OpenCourseware course.
To find the average value of a set of numbers, you just add the numbers and divide by the number of numbers. How would you find the average value of a continuous function over some interval? The problem is that there are an infinite number of numbers to add up, then divide by infinity. One approach is to divide up the interval and use n left or right samples of the value of the function, add them up, then divide by n. If we take the limit as n approaches infinity, then we will get the average value. The formula for the average value of a function, f, over the interval from a to b is average = . One way to think about this is to rewrite this formula as . Think of (b - a) as the width of a rectangle, and average as the height. Then the average value of a function on an interval is the height of a rectangle that has the same width as the interval and has the same area as the function on that interval.
Try the following:
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© Copyright 2001 David J. Eck
© Copyright 2007 Thomas S. Downey
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