Question:
Let $F= (0,0,z)$ be a vector field.
Use Gauss' Divergence Theorem to calculate the volume of the ellipsoid $x^2+y^2+2z^2=1$
My attempt:
$$r(a,b) = (\cos(a)\cos(b),\cos(a)\sin(b), \frac{\sin(a)}{\sqrt{2}})$$
where $a\in[-\frac{\pi}{2},\frac{\pi}{2}] , b\in [0,2\pi]$
I assume I must calculate $$\iint_SF \cdot \hat n \space dS= \iint_S F(r(a,b) \cdot (r_a \text{x} r_b) dadb$$
Is this a correct method?
Thank you