# How do you find the average value of the function for f(x)=sinx, 0<=x<=pi?

Feb 24, 2017

$\text{Avg value} \approx .63662$

#### Explanation:

Use the average value formula where the average value of a function $f \left(x\right)$ on the closed interval $\left[a , b\right]$ is:
$\frac{1}{b - a} {\int}_{a}^{b} f \left(x\right) \mathrm{dx}$

So, plug in our function $f \left(x\right) = \sin x$ over the interval $\left[0 , \pi\right]$:

$\frac{1}{\pi} {\int}_{0}^{\pi} \left(\sin x\right) \mathrm{dx}$

$= \frac{1}{\pi} {\left[- \cos x\right]}_{0}^{\pi}$

$= \frac{1}{\pi} \left[\left(- \cos \pi\right) - \left(- \cos 0\right)\right]$

$= \frac{1}{\pi} \left[\left(1\right) - \left(- 1\right)\right]$

$= \frac{2}{\pi}$

$\approx .63662$