Here's the question:
So using Green's Theorem, I got that the integral is equal to
\int_{C}\frac{\partial}{\partial x}(-e^xsiny) - \frac{\partial}{\partial x}(e^xcosy)dxdy = 0.
But surely the answer can't be 0? What am I doing wrong?
Can someone please explain to me why
\epsilon_{ijk}\frac{\partial}{\partial x_i}\frac{\partial A_k}{\partial x_j} = 0
where A is a constant vector field.