Answer
The divergence is positive for the points above the region $x+y=0$ and negative for the points below the region $x+y=0$.
Work Step by Step
The Divergence Theorem states that $\iint_S \overrightarrow{F}\cdot d\overrightarrow{S}=\iiint_Ediv \overrightarrow{F}dV $
Here, $S$ is a closed surface and $E$ is the region inside that surface.
$div F=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}=\dfrac{\partial (x^2)}{\partial x}+\dfrac{\partial y^2}{\partial (x+y^2)}=2x+2y=2(x+y)$
Hence, the divergence is positive for the points above the region $x+y=0$ and negative for the points below the region $x+y=0$.
