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 June 21st, 2019, 08:15 AM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 728 Thanks: 98 Evaluate integral $\displaystyle I(x,y,z)=\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} e^{-x^{2} -y^{2} -z^{2} }dz\; dy \; dx .$
 June 21st, 2019, 10:39 AM #2 Senior Member   Joined: Dec 2015 From: somewhere Posts: 728 Thanks: 98 $\displaystyle I(x,y,z)=I(x)\cdot I(y) \cdot I(z)=I^{3}(t)$. $\displaystyle I(x,y,z) =(\int_{-\infty }^{\infty} e^{-t^{2}})^{3}=\pi^{3/2}$. Thanks from topsquark

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