A fluctuating current (i) is given at time (t) by the function?

Question

i(t)=2sin3t-10cos3t

find the root mean square value of the current between t = 1.11 and t = 4.59

Answer 1

First, square the function. (Multiply it by itself.)
Then find the average by integrating over the time domain (from 1.11 to 4.59), and dividing by the elapsed time (4.59-1.11).
Next, take the square root of the result.

RMS is called root mean squared because you do just that. It's the square root of the mean of the squared function.
So, you square the function to get everything as a positive value. Then you average it by taking the mean. And finally, you take the square root (because you squared the function earlier).