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[tex]\int e^{-x^2} dx[/tex]if that can't be expressed in terms of elementary functions, how did they compute

[tex] \int ^{\infty} _{- \infty} e^{-x^2} dx =\sqrt{\pi}[/tex]

(I think I have the limits wrong, but I know it has [itex]\infty[/itex] as the upper or lower limit)