Why does $$ \int_{\Bbb R^{3N}}\Bigg[\prod_i^{3N} e^{x_i} \Bigg] d^{3N}x $$ factor into $$ \prod_i^{3N} \Bigg[\int_{-\infty}^{\infty} e^{x_i} dx_i \Bigg]$$ c.f. ideal gas in canonical ensemble in statistical physics. Is this a property of the exponential function? If so, can someone point me to it's definition?
2026-04-02 02:09:25.1775095765
Exchanging integral and product
290 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in INTEGRATION
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