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What is the circular symmetry principle of surface integral, how to use it and under what conditions?
What is the circular symmetry principle of surface integral, how to use it and under what conditions?

It means that when the letters of two variables in the surface equation are reversed, the surface remains unchanged, and when the letters are reversed, the integral values of the first kind of surface integral are equal. This is the rotational symmetry of the first kind of surface integral.

Such as: the surface is x? +y? +z? =a? When the letters of two variables in the surface equation are reversed and the surface is unchanged, then,

Then for the first kind of surface integral, the two letters are reversed and the integral value is equal. For example:

∫∫x? dS=∫∫y? dS=∫∫z? dS= 1/3∫∫(x? +y? +z? )dS= 1/3a? ∫∫dS= 1/3a? x4πa? =4/3πa? Answer?

Another example is ∫xdS =∫ydS =∫zdS.