Question

Calculate the Integral over the bounded region:
\[f(x,y,z)=e ^{-x-y-z}, B=\left\{ 0\le x, 0\le y, 0\le z \right\}\]

Answer 1

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

Answer 2

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