# How to compute the integral over these regions

Define $B(0,r)=\{u=(x,y,z)\in\mathbb R^3\colon|u|\le r^2\}$ for $r>0$.

Let $R\subset B(0,2)$ be the region such that $|u|\le 4$ and $x\le\sqrt 3$. Let $S\subset B(0,2)$ be the region with $|u|\le 4$ and $x\le\sqrt 3$ and $z\le\sqrt 3$.

How can I compute the volume of $R$ and the Volume of $S$? I don't know how to determine the bounds of the integral.

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