I have the following problem:
Compute the integral $\int_{\partial A} \langle F,\nu \rangle dS$ where $\nu$ is the normal vector and $$F(x,y,z)=(2x-3y+z,\,\,\,x-y-z,\,\,\,-x+y+2z)$$ and $$A=\{(x,y,z): |x-y|\leq 1, |y-z|\leq 1, |x+z|\leq 1\}$$
Since we have the topic "Gaussian Integral formula" I think that maybe one can compute it with the formula, but to do so, $A$ needs do be compact and have a smooth edge. I don't know how to check this. Otherwise I need to compute it directly, but then I struggle to work with the set $A$. They gave us a hint to use coordinate transformation, but I don't see where.
Could someone please help me?
With the comments from below I tried to solve it again, while solving it I remarked that the were some thinking errors from my side which were hopfully all corrected in the following image, maybe someone can have a look at the image to tell me if this works or if I have more errors.
Thank you very much.
