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I need to calculate the flux $F(x,y,z)=(x+yz,y+xz,z+xy)$ outgoing from the boundary $\vartheta D$ of :

$D = ${$(x,y,z)\in R^3 : z \ge \sqrt{x^2+y^2} $ , $x^2+y^2+z^2 \le 4 $}

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    This is very nice with the divergence theorem (https://en.wikipedia.org/wiki/Divergence_theorem) since your $\nabla \cdot F$ is constant. Just multiply it by the volume of $D$. – 2017-02-19
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    How do I calculate the volume D ? – 2017-02-19

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