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Why can the Gaussian formula of coordinate surface integral directly replace the denominator in higher mathematics, such as drawn lines?
Answer: A spherical surface Sε with the origin as the center and ε as the radius is added to remove the singularity of the integrand function (this is called the coordinate origin) and make the integral area of the integrand function a simply connected area to meet the conditions of applying the Gaussian formula. Therefore, through the application of Gaussian formula (the integral of the volume part is 0), the original ellipsoid area fraction of the coordinate axis is transformed into the small spherical surface Sε area fraction of the coordinate axis. On this small sphere, the denominator of the integrand always exists (x 2)+(y 2)+(z 2) = ε 2, which is a constant, so it can be put forward beyond the integral symbol.