If $\vec{u}=4y\hat{i}+x\hat{j}+2z\hat{k}$, calculate the double integral
$\iint(\nabla \times \vec{u})\cdot d\vec{s}$ over the hemisphere given by,
$x^{2}+y^{2}+z^{2}=a^{2}, \quad z\geq 0.$
I approached it like this, $d\vec{s}$ can be resolved as $ds\vec{n}$ where $\vec{n}$ is the normal vector to the differential surface. Which translates the integral into the surface integral in Divergence Theorem of Gauss, which implies the volume integral will be Div of Curl of u, but this Div(Curl u) is zero. I dont think this question is this trivial
Help appreciated Soham