Calculating the RMS Voltage of a Triangle Wave: Derivation and Integration

[Nothing000]

What the RMS voltage is of a triangle wave?

I am supposed to derive it. I am coming up with $$\frac{2}{T}\sqrt{V_{m}$$

 

[Nothing000]

Here is the derivation I did. Where it says $$\{n | n \in Z \}$$ I meant to say "for some integer n", I was just trying to be fancy, but I guess that's the incorrect notation.

I am attempting to upload a better image. Hopefully this is better:

 

[Nothing000]

Crap, I didn't square $$v(t)$$ in the radical.
Damn it!

Does anyone see anything else wrong?

 

[Integral]

I am uncomfortable with your definition of the triangle waveform. I would define the function and express your limits of integration in terms of the period. To be more general you may need to avoid using 0 as one extreme of the waveform.

So for example the first part would be :
$$v = \frac {4(v_m - v_0)t} T + v_0$$
With
$$0 \leq t \leq \frac T 4$$

I based this on the coordindate pair
$$(v_0, 0) ; (v_m , \frac T 4)$$

So this waveform would have miminums of $v_0$ at 0 , $\frac T 2$ and $T$

and maxs of $v_m$ at $\frac T 4$ and $\frac {3T} 4$

 

[Nothing000]

When you say definition of triangle waveform are you referring to the definition of v(t) at the top of the page?
Because this information is given to us just like that, except it says "for integer n" instead of the notation $$\{n | n \in Z \}$$ which I incorectly used.

 

[Integral]

Ok, so that is a definition of a specific triangle wave, under that definition, isn't T=1 ?

Given that that the problem is simple, square each part of the function and integrate.