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) dx∧dy

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

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