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Given that $\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$, the value of $$ \int_{-\infty}^{\infty}  \int_{-\infty}^{\infty} e^{-(x^2+xy+y^2)} dxdy$$ is

  1. $\sqrt{\pi/3}$
  2. $\pi/\sqrt{3}$
  3. $\sqrt{2 \pi/3}$
  4. $2 \pi / \sqrt{3}$
in Calculus by Veteran (431k points)
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