What is the average value of $-x^{2}+3$ on the interval $[0,6] ?$

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∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the definite integral of the function $-x^2 + 3$ from 0 to 6. ‖ ‖ step 2 ⋮ The result from step 1 is $-54$. ‖ ‖ step 3 ⋮ Divide the result from step 2 by the length of the interval, which is $6 - 0 = 6$. ‖ ‖ step 4 ⋮ The average value is $\frac{-54}{6} = -9$. ‖ ∻Answer∻ ⚹ The average value of $-x^{2}+3$ on the interval $[0,6]$ is $-9$. ⚹ ∻Key Concept∻ ⚹Average Value of a Function⚹ ∻Explanation∻ ⚹The average value of a continuous function $f(x)$ on the interval $[a,b]$ is given by $\frac{1}{b-a}\int_{a}^{b} f(x) dx$.⚹◊What is the formula for finding the average value of a function on a given interval in calculus?⍭ Generate me a similar question◊

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