Generalizing to Higher Dimensions: Stokes' Theorem is about a surface inside of${\mathrm{ℝ}}^3$. But the essence of the theorem has to do with integrating over a surface, and does not use any properties that ${\mathrm{ℝ}}^3$has which ${\mathrm{ℝ}}^4$does not.

- How would a version of Stokes' Theorem for${\mathrm{ℝ}}^4$need to change to accommodate the extra dimension?

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