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So I am trying to understand surface integrals so I can can more insight to understand Gauss's Law.

I am reading a book about it, and the example that is used to explain a surface integral is to have a flat surface that has a mass density that changes as a function of position in the x & y position σ(x,y)

The author then goes on to say that to find the total mass of the surface, take the area density and multiply by the area, and to make a summation of small areas.

The author says ''the smaller you make the area segments, the closer this gets to the true mass, since your approximation of constant σ is more accurate for smaller segments.

I don't understand this statement, if the area density changes with x & y, how can I say that the area in some corner that is very dense is approximately equal to another corner that is much less dense.

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# Surface integral - I don't understand it

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