Find the average value of the function $f (x) = x^{2} - 9$ on $[0, 9]$
The average value of the function $f (x) = x^{2} - 9$ on $[0, 9]$ is

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Final Answer: The average value of the function $f (x) = x^{2} - 9$ on $[0, 9]$ is $18$ .

Steps

Step 1 ：The average value of a function $f (x)$ on the interval $[a, b]$ is given by the formula: $\frac{1}{b - a} \int_{a}^{b} f (x) d x$

Step 2 ：We need to find the average value of the function $f (x) = x^{2} - 9$ on $[0, 9]$ .

Step 3 ：To do this, we compute the integral of $f (x)$ from 0 to 9 and then divide by 9-0.

Step 4 ：The result of this calculation is 18.

Step 5 ：Final Answer: The average value of the function $f (x) = x^{2} - 9$ on $[0, 9]$ is $18$ .