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Finding the Average Value of a Function

on the TI-89

If the function f is continuous (and differentiable) on [a, b], the average value of f on [a, b] is:

y_bar = (1/(b-a))int(f(x), dx, a, b)

Although this is a simple and straightforward calculation, it can be handy to have it in function form to use for quick checks. The function is:

Define aveval(f,x,a,b)= int(f,x,a,b)/(b-a)

If you don't remember how to enter a user-defined function on the TI-89, click here. The average value of a function is (very) closely related to the Mean Value Theorem.

The screen shot on the left shows a solution to the problem. "Find the average value of f(x) = sin(x) on the interval [0, pi]." The screen shot at right shows a graph of this function together with the line y = 2/ on the same interval.

Screen shot for aveval(sin(x),x,0,pi) = 2/pi

graph of y=sin(x) and y = 2/pi

last update January 28 2004 by JL Stanbrough