## Calculus: Early Transcendentals 8th Edition

The divergence is positive for the points above the region $x+y=0$ and negative for the points below the region $x+y=0$
Divergence Theorem: $\iint_S \overrightarrow{F}\cdot d\overrightarrow{S}=\iiint_Ediv \overrightarrow{F}dV$ Here, $S$ shows a closed surface and $E$ is the region inside that surface. $div F=\dfrac{\partial p}{\partial x}+\dfrac{\partial q}{\partial y}+\dfrac{\partial r}{\partial z}=2x+2y=2(x+y)$ Hence, the divergence is positive for the points above the region $x+y=0$ and negative for the points below the region $x+y=0$.