# How do you find the average value of the function

How do you find the average value of the function for $f\left(x\right)=\mathrm{sin}x,0\le x\le \pi$?
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Nicolas Calhoun
Explanation:
Use the average value formula where the average value of a function f(x) on the closed interval [a,b] is:
$\frac{1}{b-a}{\int }_{a}^{b}f\left(x\right)dx$
So, plug in our function $f\left(x\right)=\mathrm{sin}x$ over the interval $\left[0,\pi \right]:$
$\frac{1}{\pi }{\int }_{0}^{\pi }\left(\mathrm{sin}x\right)dx$
$=\frac{1}{\pi }\left[-\mathrm{cos}x{\right]}_{0}^{\pi }$
$=\frac{1}{\pi }\left[\left(-\mathrm{cos}\pi \right)-\left(-\mathrm{cos}0\right)\right]$
$=\frac{1}{\pi }\left[\left(1\right)-\left(-1\right)\right]$
$=\frac{2}{\pi }$
$\approx .63662$