Mean of a function Mean

in circumstances mathematicians may calculate mean of infinite (even uncountable) set of values. can happen when calculating mean value




y

ave




{\displaystyle y_{\text{ave}}}

of function



f
(
x
)


{\displaystyle f(x)}

. intuitively can thought of calculating area under section of curve , dividing length of section. can done crudely counting squares on graph paper or more precisely integration. integration formula written as:

y

ave


(
a
,
b
)
=




∫

a


b



f
(
x
)

d
x



b
−
a





{\displaystyle y_{\text{ave}}(a,b)={\frac {\int \limits _{a}^{b}\!f(x)\,dx\,}{b-a}}}

care must taken make sure integral converges. mean may finite if function tends infinity @ points.