## anonymous 5 years ago Calculate the Integral over the bounded region: $f(x,y,z)=e ^{-x-y-z}, B=\left\{ 0\le x, 0\le y, 0\le z \right\}$

1. anonymous

$f(x,y,z)=e^{-x-y-z}, B=\left\{ 0\le x, 0\le y, 0\le z \right\}$

2. anonymous

$\iiint\limits_{B}e^{-x-y-z}dxdydz=\int\limits_{0}^{+\infty}e^{-x}dx\cdot\int\limits_{0}^{+\infty}e^{-y}dy\cdot\int\limits_{0}^{+\infty}e^{-z}dz=1$

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