Mean
Mean of a function

In some circumstances, mathematicians may calculate a mean of an infinite (or even an uncountable) set of values. This can happen when calculating the mean value y avg {\displaystyle y_{\text{avg}}} of a function f (x) {\displaystyle f(x)}. Intuitively, a mean of a function can be thought of as calculating the area under a section of a curve, and then dividing by the length of that section. This can be done crudely by counting squares on graph paper, or more precisely by integration. The integration formula is written as:

In this case, care must be taken to make sure that the integral converges. But the mean may be finite even if the function itself tends to infinity at some points.
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