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#