Consider the circle in the $xz$-plane with center at $x = 5$, $z = 0$ and radius $3$. If $S$ is the surface generated by rotating the circle around the $z$-axis.
I am asked to orient S with unit normal vectors pointing away from the inside of the torus. Given this how can I set the integral for $$\iint_S(x \mathbf{i} + y\mathbf{j})\cdot d\mathbf{A}$$
So far I have just gotten a parametrization of S
$S=((5+3\cos(t))(\cos (\theta),(5+3\cos(t))(\sin (\theta),3\sin (t))$