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Calculus Level 5

If

\[\displaystyle\int_{-\infty} ^{\infty}\displaystyle\int_{-\infty} ^{\infty}\displaystyle\int_{-\infty} ^{\infty} e^{-x^2-y^2-z^2}\ dx \ dy \ dz\]

Can be expressed as

\[\ Pi(x) \times \sqrt{k} \pi\]

Find the value of \(k\)


\[\ Pi(x) =\displaystyle\int_0^{\infty} e^{-x^{2}} \ dx\]

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