Find the average value of the function $f$ over the interval $[-3,5]$.
\[
f(x)=9-x^{2}
\]

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Final Answer: The average value of the function $f(x)=9-x^{2}$ over the interval $[-3,5]$ is $\boxed{\frac{8}{3}}$.

Steps

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

Step 2 ：In this case, $a = -3$, $b = 5$, and $f(x) = 9 - x^{2}$. So, we need to calculate the integral of $f(x)$ from $-3$ to $5$, and then divide the result by $b - a = 5 - (-3) = 8$.

Step 3 ：The average value of the function over the interval $[-3,5]$ is calculated to be $\frac{8}{3}$.

Step 4 ：Final Answer: The average value of the function $f(x)=9-x^{2}$ over the interval $[-3,5]$ is $\boxed{\frac{8}{3}}$.

Find the average value of the function $f$ over the interval $[-3,5]$.\[f(x)=9-x^{2}\]

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Find the average value of the function $f$ over the interval $[-3,5]$.
\[
f(x)=9-x^{2}
\]