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

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Answer 1 · 2017-02-24T04:35:05

$"Avg value"approx .63662$

Use the average value formula where the average value of a function $f(x)$ on the closed interval $[a,b]$ is:
$1/(b-a)int_a^bf(x)dx$

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

$1/(pi)int_0^pi(sinx)dx$

$=1/pi[-cosx]_0^pi$

$=1/pi[(-cospi)-(-cos0)]$

$=1/pi[(1)-(-1)]$

$=2/pi$

$approx .63662$

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