# Chapter 16: Integrals and Vector Fields - Section 16.8 - The Divergence Theorem and a Unified Theory - Exercises 16.8 - Page 1025: 8

$$= 32 \pi$$

#### Work Step by Step

We know that $$div F=\dfrac{\partial P}{\partial x}i+\dfrac{\partial Q}{\partial y}j$$ From the given equation, we have $$Flux =\iiint_{o}(2x+3) \space dz \space dy \space dx \\ =\nabla \cdot F \\=\int_{0}^{2\pi}\int_{0}^{\pi}\int_{0}^{2} (2 \rho \sin \phi \cos \theta+3) \space (\rho^2 \sin \phi) \space d\rho \space d\phi \space d\theta \\ =\int_{0}^{2 \pi}(4 \pi \cos \theta +16) d\theta \\= 32 \pi$$

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