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I am learning to apply the differential form of Gauss's law and found an article titled Differential form of Gauss's law to learn it from.

However, in the paragraph that explains equation (6) in the article, the author says "....,the integrals can be replaced by" and introduces a new expression without the integrals. Is it related to the fundamental theorem of calculus?

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The author is taking the limit as the volume of integration goes to zero. Any integral of a proper function (not distributions like Dirac deltas) over a zero-size region is zero.

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