Disclaimer: I’m a total beginner in GA (and in general mathematics), so if I’m saying something too wrong please or oblivious, please forgive me.

I’m reading the GA book for Electrical Engineers of Peeter Joot, and he introduces the generalized Stokes theorem:

\int_V d^k\cdot(\partial \wedge F) = \int_{\partial V} d^{k-1}\cdot F

Following the given proof, by grade selection on the fundamental theorem of GA, it seems to me that also the dual formulation should be right, doing similar proving steps:

\int_V d^k\wedge(\partial \cdot F) = \int_{\partial V} d^{k-1}\wedge F

So, is this formula known/correct?

Does this formula as a name?

Thanks for any help.