Answer
$2 \pi$
Work Step by Step
$div F=\dfrac{\partial P}{\partial x}+\dfrac{\partial q}{\partial y}+\dfrac{\partial r}{\partial z}=4 \sqrt {x^2+y^2+z^2}$
Now, we have
$Flux=4 \times \int_{0}^{2 \pi}\int_0^{\pi/2} \int_{0}^{1} 4 \sqrt {x^2+y^2+z^2} dV$
$=4 \times \int_{0}^{2 \pi}\int_0^{\pi/2} \int_{0}^{1} \sqrt{\rho^2} \rho^2 \sin \phi d \rho d\phi d \theta$
$=4 [\int_{0}^{2 \pi} d\theta] \cdot [\int_0^{\pi/2} \sin \phi d\phi] \cdot [\int_{0}^{1}[\rho^3 d \rho] $
$=4 (2 \pi) \times (-\cos \phi)_0^{\pi/2} \times [\dfrac{\rho^4}{4}]_0^1$
$=(8 \pi) \times [-(\cos (\pi/2)-\cos 0)] \times [\dfrac{(1)^4}{4}-0]$
$=2 \pi$
