Average value for a function over its entire domain

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Saeed.z
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As we know , the average value of a function
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over
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is :
Formula for the average value of f(x) over [a, b]: 1/(b - a) times the integral from a to b of f(x) dx.


i wanted to calculate the average value of a function over its entire domain ( e.g
Interval notation (-∞, ∞) showing the entire real line as the domain.
)

firstly, i divided the interval into 2 intervals
Interval (-∞, 0] written in interval notation.
&
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and calculated the F_avg for each ,,, is my way correct ? thanks !
 
yes, then you'll need to average the two averages.
 
^

thanks !

but if we assumed t= infinity and take the limit so it'd be :

Forum error box reading "Invalid Equation" with a red exclamation icon.


is it correct ? thanks again !