was wondering if you can help me understand something.

This diagram here shows a sinusoidal leading edge phase controlled voltage. I need to determine the RMS value as a function of the phase angle β.

The formula for RMS is sqrt(1/T * definite integral (T to 0) of mean^2)

The answers give

Now, I figure that this answer can be achieved if the formula for RMS is sqrt(Vpeak^2 * indefinite integral sin^2(pi * t + b))

My question: is this correct? and if it is, why the integral is indefinite? why it is not over a period 1/T? because every time I am doing the definite integral, all the stuff gets cancelled and I end up with just Vpeak/sqrt(2) (which is what you would expect for a sine wave, I suppose). Also, why is the angle represented as (pi * t + b)? Normally, it's omega*t + b, but in this case x-axis is already omega*t, so I guess it can be related to this... What I really need is to understand the task and the graph for any similar problems in future, as I am not sure when I am supposed to use definite integral and when indefinite and for which cases