If the function f is continuous (and differentiable) on [a, b], the average value of f on [a, b] is:
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:
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.
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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, |
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The screen shot at right shows a graph of this function
together with the line y = 2/