Lydia Carey

2022-06-29

What is the average value of a function $\mathrm{sin}\left(X\right)$ on the interval $\left[0,\pi \right]$?

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Expert

Average $=\frac{\int \mathrm{sin}xdx}{\pi }$, over the interval $\left[0,\pi \right]$
The denominator is the length of the interval of integration.t.
$=\frac{-\mathrm{cos}x}{\pi }$, between the limits $\left[0,\pi \right]$
$-\left[-\mathrm{cos}\pi -\mathrm{cos}0\right]$
$=-\frac{-1-1}{\pi }=\frac{2}{\pi }$

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