The time average of a function is found by evaluating the integral:

with the average taken over a time, ΔT.

Time averages are often important when considering oscillating waves of the form:

where ω is the angular frequency and *A* is the amplitude. The instantaneous value of this wave varies between *-A* and *A*, however, the time average of this wave over one period is .

Another common example (such is in the calculation of the intensity of an electromagnetic wave) is to find the time average of the functions

and |

Using the equation (1) above, it can be shown that:

.

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