Ayaan Barr

2022-07-15

What is the average value of the function f(x)=18x+8 on the interval [0, 10]?

eurgylchnj

Expert

The average value of f on [a,b] is
$\frac{1}{b-a}{\int }_{a}^{b}f\left(x\right)dx.$
For this problem, that is
$\frac{1}{10-0}{\int }_{0}^{10}\left(18x+8\right)dx=\frac{1}{10}\left[9{x}^{2}+8x{\right]}_{0}^{10}$
$=\frac{1}{10}\left[980\right]=98$

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