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June 21st, 2019, 08:15 AM   #1
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Evaluate integral

$\displaystyle I(x,y,z)=\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} e^{-x^{2} -y^{2} -z^{2} }dz\; dy \; dx .$
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June 21st, 2019, 10:39 AM   #2
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$\displaystyle I(x,y,z)=I(x)\cdot I(y) \cdot I(z)=I^{3}(t)$.
$\displaystyle I(x,y,z) =(\int_{-\infty }^{\infty} e^{-t^{2}})^{3}=\pi^{3/2}$.
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