Trapezoidal wave RMS value
The formulas for both the waveform and the RMS calculations have typos. For the waveform's first and last intervals, there is an extra minus in the 2nd terms. The terms should be:
$$\begin{align}
&amp;\dfrac{2A}{u}(-\pi-t)\tag{1} \\
&amp;\dfrac{2A}{u}(\pi-t)\tag{2}
\end{align}$$
Strangely enough, the way they are written in the integrands is fine, but the result is off in the last integration, it should be the same result as in the first integration:
$$\dfrac{A^2u}{12\pi}\tag{3}$$
Now, if you calculate the sum for the RMS:
$$A\sqrt{2\dfrac{u}{12\pi}+2\dfrac{\pi-u}{2\pi}+\dfrac{u}{6\pi}}=A\sqrt{\dfrac{u}{3\pi}+\dfrac{\pi-u}{\pi}}\tag{4}$$
And if you replace \$u=\pi/6\$ and \$A=12\$:
$$\begin{align}
12\sqrt{\dfrac{\pi}{6}\dfrac{1}{3\pi}+\dfrac{\pi-\dfrac{\pi}{6}}{\pi}}&amp;=12\sqrt{\dfrac{1}{18}+\dfrac{5\pi}{6}\dfrac{1}{\pi}} \\
&amp;=12\sqrt{\dfrac{1}{18}+\dfrac{5}{6}} \\
&amp;=12\sqrt{\dfrac{16}{18}} \\
&amp;=\dfrac{12}{3}\cdot 2^{\frac{3}{2}} \\
&amp;=\dfrac{3\cdot 2^2}{3}\cdot 2^{\frac{3}{2}} \\
&amp;=2^3\cdot 2^{\frac12} \\
&amp;=8\sqrt{2} \tag{5}
\end{align}$$
Sorry for the lengthy noobish arithmetic, just wanted to be sure it's clear enough how to reach Spehro Pefhany's result.