I have a vector field over a tetrahedron with vertices at and and I need to compute being the surface of the tetrahedron.
I have already calculated , which I have found to be equal to , now I need to calculate the previous integral and assumedly show that the answers agree (Gauss' Theorem).
So far I have parameterised the surface to say
Next I find as such:
But, upon calculating the integral I get . I'm confident in my first integral, but I don't feel as confident in this one as I feel there may be some theoretical misunderstanding with my parameterisation. Any help is appreciated.