Average Value of a Function

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$Average Value of a Function Example 1$

$Average Value of a Function Example 2$

$Average Value of a Function Example 3$

The average value of a function on the interval $[a,b]$ is given by

$\frac{1}{b-a}\int_a^b f(x)\ dx$

This formula will tell you the average value (height) of the function between $x=a$ and $x=b$ .

Problems that ask you to find the average value of a function will give you the function and the range on which to evaluate it. Sometimes the range will be given to you as $[1,3]$ , or sometimes the range will be attached to the integral of the function, with the lower bound as $1$ and the upper bound as $3$ .

Just plug the function into the integral, plug in the upper bound for $b$ , and plug in the lower bound for $a$ . Then just evaluate the definite integral and simplify until you get a number for your answer.

Average Value of a Function

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