Show that, for a vector field $v^a$ that vanishes on a hypersurface S enclosing a region V of an N-dimensional manifold:
$$\int_V(\nabla_av^a)\sqrt{-g}d^Nx=0$$ Where $g$ stands for the determinant of the metric.
This is one of the maths exercises on my physics book, and it puzzles me to the point that I don't even know where to start on, so even a hint will do!