$E$ is a closed smooth surface in $\mathbb R^3$, $F(x,y,z)=(3x,(x^2+z^2)y^2,(x^2+y^2)z^2)$ and $n$ is the outer unit normal. Question says find the volume enclosed by $E$ given that $\int_E F\cdot ndS=1$.
I guess I misinterpret or miss an important thing. Because when I apply Divergence Theorem, I only get $$ 3V(\Omega)+2\int_\Omega (x^2+z^2)2y+(x^2+y^2)2z dV=1$$ where $\Omega$ is the volume enclosed by E.
It looks like this is not a sufficient to determine $V(\Omega)$.
So, my question is: how should I approach to this problem and what do I miss or misunderstand? I'd be glad for any help.