So there is something I don't understand here, I have to calculate the flux over the triangle with vertices (1, 0, 0) , (0, 1, 0), (0, 0, 1).
Where \begin{equation} \vec A = (xy, yz, zx)\end{equation} So \begin{equation} \phi = \oint_C \vec A \cdotp \,d\vec s\ = \oint_c xydx +yzdy + zxdz = \iint_S \nabla \times\vec A \cdot dS \end{equation}
The tranformation used is
\begin{equation} \begin{cases} x = u -v\\ y = 1 - u - v\\ z = 2v \end {cases} \end{equation}
In my answer I used \begin{equation} \begin{cases} x = u\\ y = v\\ z = 1-u-v\\ \end{cases} \end{equation}
But I end up with a different answer. I think it has to do with the way I parametrized it?