anonymous
  • anonymous
\[\int_{-inf}^{inf} e^{-x^2}e^{-x y} dx\]
Mathematics
chestercat
  • chestercat
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chestercat
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anonymous
  • anonymous
@myininaya ,@amistre64
anonymous
  • anonymous
I think this is the solution\[e^{\frac{y^2}{4}}\sqrt{\pi}\]
anonymous
  • anonymous
show the work; I am not interested in solution

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anonymous
  • anonymous
@zarkon
anonymous
  • anonymous
@Jemurray3
anonymous
  • anonymous
\[ \large \int_{-\infty}^\infty e^{-x^2} e^{-xy} dx = \int e^{-(x^2+xy)}dx = e^{y^2/4}\int e^{-(x^2+xy+y^2/4)}dx\] \[ \large = e^{y^2/4}\int e^{-(x+y/2)^2}dx = \sqrt{\pi}\cdot e^{y^2 / 4}\]
anonymous
  • anonymous
how did you get \[\int e^{-(x^2+xy)}dx = e^{y^2/4}\] ?
anonymous
  • anonymous
I didn't. I multiplied the integrand by exp(-y^2/4) and to compensate multiplied the outside by exp(y^2/4).
anonymous
  • anonymous
thanks, man
anonymous
  • anonymous
Sure

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