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

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Accepted Answer

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}).

Answer

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}).

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

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