Why Do We Use Squaring Instead of Absolute Value in Signal Power Calculations?

[LLT71]

in terms of calculating energy and power, why don't we use absolute value of signal and then integrate it from -inf to +inf instead of squaring it and then integrating it over -inf to +inf?
for example ∫|sinx|dx (from -inf to +inf) will give you, relatively speaking, the same answer as ∫[sinx]^2dx (from -inf to +inf).

what is physical significance of determining if signal is power or energy one? what those two quantities tell you besides if signal is periodic/non-periodic?

 

[berkeman]

in terms of calculating energy and power, why don't we use absolute value of signal and then integrate it from -inf to +inf instead of squaring it and then integrating it over -inf to +inf?
for example ∫|sinx|dx (from -inf to +inf) will give you, relatively speaking, the same answer as ∫[sinx]^2dx (from -inf to +inf).

what is physical significance of determining if signal is power or energy one? what those two quantities tell you besides if signal is periodic/non-periodic?

Are you integrating voltage, current or power?

 

[LLT71]

Are you integrating voltage, current or power?

please sorry in advance for my ignorance! in my Signal Processing textbook it says that for every continuous signal we define energy of signal as ∫|[x(y)^2]|dx so, since I'm new at this I presume it stands for "any signal".

 

[sophiecentaur]

A couple of points here. If you integrate (+-∞) an AC Voltage or Current signal, the result is Zero.
The reason for using Mean Square or Root Mean Square is that you very seldom have both V and I signals available. RMS gives you the (Average) Power that your Voltage waveform will dissipate in a resistive load without Integrating VI (which is not zero because both signs change at the same time to produce positives for each half of the cycle).
Power = V²R or I²R, whichever you choose or can measure.
We normally deal with Power, in these cases and that is the Average over a specific time (a number of whole cycles of the waveform ). So your Integration is not +-∞.