Caleb Proctor

2022-07-10

What is the average value of a function $\mathrm{sin}x$ on the interval $\left[0,\frac{\pi }{3}\right]$?

Hayley Mccarthy

Expert

$k=\frac{1}{b-a}{\int }_{a}^{b}f\left(x\right)dx$
$k=\frac{1}{\frac{\pi }{3}}{\int }_{0}^{\frac{\pi }{3}}\mathrm{sin}xdx$
$k=\frac{3}{\pi }\left[|-\mathrm{cos}x{|}_{0}^{\frac{\pi }{3}}\right]$
$k=\frac{3}{\pi }\left[-\mathrm{cos}\left(\frac{\pi }{3}\right)+\mathrm{cos}0\right]$
$k=\frac{3}{\pi }\left[-\frac{1}{2}+1\right]$
$k=\frac{3}{\pi }\ast \frac{1}{2}$
$k=\frac{3}{2\pi }$

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