crutschow:
Sorry, But you need RMS of V and RMS of I to get power factor and RMS of V * I
If the signals are super clean and you take the Nyquest theorem seriously (either line frequency or sample frequency), you would still need timing info if you had the peaks. Signal period (frequency isn't always 60 Hz), peak I, peak V, when the peak occurred) and we ASSUME it's a pure sine wave.
If you timed the difference between the current and voltage peaks and know the frequency, you could determine phase angle. For the power line, the frequency is not constant. Pretty close to a constant, but not a constant. There are experiments being done to make it more sloppy and plants have had to install generators to compensate.
This should be required reading:
https://www.analog.com/library/analogDialogue/archives/33-02/power/index.html
The Calculus is noting but multiplying and summing. Numerical integration is the sum of all the little rectangles under the curve.
e.g. sum(v(t) * i(i) delta(t)); since it's rms, the bottom part of the wave form is fllipped, so everything is positive. Now you have to divide that integration by the total time.
So now you have other issues: Is this an energy meter? What interval will power be taken over ( average over last 10 cycles)? What interval will "instantaneous power" be taken from (1 cycle)?