How do you find the average value of #sinx# as x varies between #[0,pi]#?

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Answer 1 · 2016-11-26T14:16:40

#2/pi#

The average value of a function #f# on the interval #[a,b]# is found through the integral expression

#1/(b-a)int_1^bf(x)dx#

Here, this gives us an average value of

#1/(pi-0)int_0^pisin(x)dx#

The antiderivative of #sin(x)# is #-cos(x)#:

#=1/pi[-cos(x)]_0^pi#

#=1/pi(-cos(pi)-(-cos(0)))#

#=1/pi(-(-1)-(-1))#

#=2/pi#