Chapter 15 - Section 15.8 - The Divergence Theorem and a Unified Theory - Exercises - Page 906: 7

$ -8 \pi$

As we know that $div F=\dfrac{\partial A}{\partial x}i+\dfrac{\partial B}{\partial y}j+\dfrac{\partial C}{\partial z}k$ Now, we have $Flux =\iiint_{o}(x-1) dz dy dx$ Also, $Flux =\nabla \cdot F=\int_{0}^{2\pi}\int_{0}^{2}\int_{0}^{r^2} (r \cos \theta-1) dz dr d\theta$ This implies that $\int_{0}^{2 \pi}(\dfrac{32}{5} \cos \theta -4) d\theta = -8 \pi$