I have to find the power of the following signal and would like to know if I'm doing this right or, if I'm doing it wrong, how to do it.
The equation for power in my textbook is $\overline{m^2(t)} = \lim_{T\to\infty} \frac{1}{T} \int_{\frac{-T}{2}}^{\frac{T}{2}} m^2(t) dt$
This signal periodically has the equation $m(t) = \frac{t}{\pi/4} $
From the picture, $T=\pi$
Therefore, this can be simplified to: $\overline{m^2(t)} = \lim_{T\to\infty} \frac{1}{\pi} \int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} (\frac{t}{\pi/4})^2 dt$, right?
If the above is correct, then $\overline{m^2(t)} = \frac{1}{6}$
I believe this is correct, but only for the part of the signal that exists. Since half of the signal has no value or is zero, does this mean I have to divide the answer I just got by 2? So that $\overline{m^2(t)} = \frac{1}{12}$?
Your value of $\frac 16$ for the power of the signal is correct. The fact that the signal is $0$ on a part of its period doesn't change the formula.
If you had tried to use $T = \pi/2$, then you would have to divide your answer by $2$.