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#