Is dxdydx\,dy really a multiplication of dxdx and dydy?

On the answers of the question Is dydx not a ratio? it was told that dydx cannot be seen as a quotient, even though it looks like a fraction. My question is: does dxdy in the double integral represent a multiplication of differentials? The problem than can be generalized for a multiple integral.

Answer

In a double integral, you are actually integrating a differential two-form:

Rf(x,y) dxdy

Here, dx and dy are the basis differential one-forms and dxdy is their exterior product.

Attribution
Source : Link , Question Author : Emo , Answer Author : Fly by Night

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