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At first chaneg to spheric coordinates $x = rcos ( \phi)sin (\theta)$ $y = r sin (\phi)sin (\theta)$ $z = r cos(\theta)$ $dx dy dz = r^{2} sin(\theta) dr d\phi d\theta$ $0 \leq r \leq 4cos(\theta)$ $0\leq \phi \leq 2\pi$ $0\leq \theta \leq\frac{\pi}{2}$ $I=\displaystyle\int \limits^{2\pi }_{0}\displaystyle\int \limits^{\frac{\pi }{2} }_{0}\displaystyle\int \limits^{4cos\left( \theta \right) }_{0}r^{3}\left( r^{2}sin\left( \theta \right) \right) d\phi d\theta dr$ $I=\displaystyle\int \limits^{2\pi }_{0}d\phi \displaystyle\int \limits^{\frac{\pi }{2} }_{0}sin\left( \theta \right) d\theta \displaystyle\int \limits^{4cos\left( \theta \right) }_{0}r^{5}dr$ $I=2\pi\displaystyle\int \limits^{\frac{\pi }{2} }_{0}sin\left( \theta \right) \left( \frac{4^{6}cos^{6}\left( \theta \right) }{6} \right) d\theta$ $I=\frac {4096}{3} \times \frac{\pi}{7}$ $I = \frac{4096\pi}{21}$ $\text{so} A+B = 4117$