Answer
$4 \pi R^5$
Work Step by Step
Here, $div F=(x^2+y^2+z^2) \cdot \lt x,y,z \gt=3(x^2+y^2+z^2)+2(x^2+y^2+z^2)$
or, $div F=5(x^2+y^2+z^2)=5\rho^2 $
$Flux=\int_{0}^{2 \pi}\int_0^{\pi} \int_{0}^{R} 5\rho^2 dv=\int_{0}^{2 \pi}\int_0^{\pi} \int_{0}^{R} 5\rho^2 \times \sin \phi \times d \rho d\phi d \theta$
$=\int_{0}^{2 \pi}\int_0^{\pi} \int_{0}^{R} 5\rho^2 \times \sin \phi \times d \rho d\phi d \theta$
$=\int_{0}^{2 \pi}\int_0^{\pi} R^5 \times \sin \phi d \rho d\phi d \theta$
$=\int_{0}^{2 \pi} R^5 [(-\cos \phi)_0^{\pi} d \theta$
$=\int_{0}^{2 \pi} R^5 [-(\cos \pi- \cos 0] d \theta$
$Flux=4 \pi (R^5)$
