Problem

Find the average value of the function $f(x)=x^{2}-7$ on $[0,6]$.

Solution

Step 1 :The problem is asking for the average value of the function \(f(x)=x^{2}-7\) on the interval \([0,6]\).

Step 2 :The formula for the average value of a function \(f(x)\) on the interval \([a, b]\) is \(\frac{1}{b-a}\int_{a}^{b}f(x)dx\).

Step 3 :In this case, \(f(x) = x^{2}-7\), \(a = 0\), and \(b = 6\). So, we need to calculate the integral of \(f(x)\) from \(0\) to \(6\), and then divide the result by \(6-0=6\).

Step 4 :The calculation gives us an average value of 5.

Step 5 :Final Answer: The average value of the function \(f(x)=x^{2}-7\) on \([0,6]\) is \(\boxed{5}\).

From Solvely APP
Source: https://solvelyapp.com/problems/28217/

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