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I have a signal with half-amplitude $A$ and period $T$ and I want to calculate the average power of the signal.

I think I remember the power of a signal $x(t)$ to be $$\frac{1}{T}\int_{0}^{T}|x(t)|^2dt$$ but how do I apply this to a square wave?

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    $\begingroup$ Why can't you evaluate the integral you showed? $\endgroup$ – Jason R Sep 10 '14 at 19:13
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    $\begingroup$ Hint: break up the integral into the sum of integrals with limits $(0,T_1)$ and $(T_1,T)$ respectively where $T_1$ is a number that you get to choose. If you apply a modicum of sense before choosing (hint: it helps a lot to sketch the square wave first), the answer is obtained trivially, but if not... $\endgroup$ – Dilip Sarwate Sep 10 '14 at 19:37
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Hint:

What is the absolute value of a square wave? Once you get that, the integral becomes very easy.

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