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- Jan 26, 2012

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**Problem**: Let $G$ be a rectangular box defined by the inequalities $a\leq x\leq b$, $c\leq y\leq d$, $k\leq z\leq l$. Show that

\[\iiint\limits_G f(x)g(y)h(z)\,dV = \left[\int_a^b f(x)\,dx\right]\left[\int_c^d g(y)\,dy\right]\left[\int_k^l h(z)\,dz\right],\]

where $\,dV=\,dx\,dy\,dz$.

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