Imagine a rectangular pool with a bunch of random waves, frozen in time
If you take a line and follow it from some point along the width, then the motion of the waves along that one dimensional line is what you would get from an integral
But that’s only a one dimensional line on the two dimensional plane
If you took that one dimensional line and swept that along the length, you would get the motion of the waves along the plane. That’s the essence of a double integral
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