Page 284 - Basic Electrical Engineering

The RMS values of an alternating quantity of any type of wave shapes can
be calculated using analytical methods.

3.1.6 Analytical Method of Calculation of RMS Value, Average Value, and
Form Factor

Suppose we have a sinusoidal alternating current, we have to first square it,

then take its mean over one cycle or half cycle, and then take the square root
(note that RMS value is calculated by making reverse operation i.e., first

square, then take mean and then take square root).
Square of the current

Its mean over one cycle is calculated by integrating it from 0 to 2π and
dividing by the time period of 2π as follows:

Mean of square

RMS value,

To calculate, let us put

then