Find the total flux of the vector field $ F = (3x, xy,1) $
across the boundary of the box $ D = {|x| \leq 1 , |y| \leq 2, |z|\leq 3} $
Somehow, I think I know what this looks like very clearly. It's just that I'm not sure how to set up the integral for this.
So I would do something like: $ \int_A f(x) \cdot \vec{n} dA $ over each surface of my box and add them together.
Now, I'm not sure how to get n