Time average of $\cos^2 x$ function [closed]

How do I find the time average of $\cos^2(3-wt)$ ?

-

closed as too localized by Lord_Farin, Michael Albanese, 23rd, TMM, Davide GiraudoApr 26 '13 at 12:58

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Your question is phrased as an isolated problem, without any further information or context. This does not match MSE quality standards, so it may attract downvotes, or be closed. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. Making these improvements will attract more appropriate answers and make the question more valuable for future MSE visitors. – Kasper Apr 26 '13 at 11:38
What is the definition of time average, and is "w" a constant? – dezign Apr 26 '13 at 11:39
What is the definition of time average of a function? And have you seen trigonometric identities such as $2\cos^2x= 1+\cos 2x$? – Dilip Sarwate Apr 26 '13 at 11:39

For a one variable function $f(t)$ with period $T$ the time average function is defined as

$$\frac{1}{T} \int_{0}^{T} dt f(t)$$

so what you need to compute is the following integral

$$\frac{1}{T}\int_{0}^{T}dt\cos^2(3-\omega t)$$

where $T$ is the smallest strictly positive number such that:

$$f(t+T)=f(t)$$

-
Important: T is the smallest strictly positive number verifying $f(t+T)=f(t)$! – moray95 Apr 26 '13 at 11:59
@moray95 thank you – Jorge Apr 26 '13 at 12:02