The math approach can also be simplified. "RMS" is the root of the mean square. To calculate it, you take many small slices, square the voltage at each incremental slice, add up all these slices and divide by the number of slices to get the mean (or average) square value; then take the square root of that. This is a bit complex with waveforms that aren't square, but you can see by inspection that the square of +30V and -30V is always the same answer (900 volts squared) no matter how many you add up then divide by the number of addends. When you then take the square root of that mean/average square, you get 30 volts.
This is good, because Mother Nature insists that the answers come out the same...
Doing integral over a cycle with a sine wave is almost as simple after you've been extruded through integrals, but it gets complicated with any signal that's not simple and easily defined for integrating.