Hello. If one wants to compute the integral of a two form, say $\omega = y dx\wedge dy + z dy\wedge dz$ on the submanifold given by $z=16-x^2-y^2$ and $z>0$ of $\Bbb R^3$, how one approach this?
Do I reduce this to a classic calculus type double integral somehow? Perhaps something like $$\int \int (16-x^2-y^2)y dxdy + \int\int (16-x^2-y^2)z dydz,$$
with the appropriate regions (and appropriate orientations by placing an orientation on the submanifold)? Or something else entirely