How is the inverse of a volume integral denoted?

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SUMMARY

The inverse of the volume integral denoted as ∫ d³x, which represents the three-dimensional integral ∫ dxdydz, is expressed as d³V/dx dy dz. This notation indicates the differential volume V in relation to the three spatial dimensions. The discussion highlights the need for precise specification when discussing inverse integrals, particularly in higher dimensions, as the notation is not commonly encountered in standard mathematical literature.

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In 1-D the inverse of ∫ dx is dy/dx so how is the inverse of the volume integral ∫ d3x = ∫ dxdydz denoted ? Thanks
 
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One would need to specify it a lot more precisely to elevate either the 1D example you gave, or the 3D one I'll give, to the status of a function inverse. But loosely speaking, I think what you are looking for is
$$\frac{d^3V}{dx\,dy\,dz}$$
where ##V## is the volume.
 
Thanks. That makes sense but I've never seen that kind of notation before. In fact I don't think I've ever seen any notation to cover this. I just thought I was missing something obvious.
 

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