How do you find the average value of $f(x)=cosx$ as x varies between $[0, pi/2]$ ?

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Answer 1 · 2016-09-05T19:13:28

$2/pi$

The average value of the function $f(x)$ on the interval $[a,b]$ can be evaluated through the following the following expression:

$"average value"=1/(b-a)int_a^bf(x)dx$

Here, this gives us an average value of:

$1/(pi/2-0)int_0^(pi/2)cos(x)dx$

Integrating $cos(x)$ gives us $sin(x)$ :

$=1/(pi/2)[sin(x)]_0^(pi/2)$

$=2/pi[sin(pi/2)-sin(0)]$

$=2/pi[1-0]$

$=2/pi$

How do you find the average value of f(x)=cosxf(x)=cosx as x varies between [0, pi/2][0, pi/2]?