I have to calculate the flux between two paraboloids (so an enclosed region), but oriented inwards. I calculated the normal vectors, but found that the integration required was super hard. I realized that using the divergence theorem would make things a lot easier, but I am confused as to how the divergence theorem accounts for an inward or outward orientation.
I have always used the divergence theorem to calculate flux of a region with an outwards orientation. Is it as simply as multiplying by -1 to the flux or am I missing something.