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How to solve the following $$\iint\limits_{x^2+y^2\ge k}\frac{\exp(-(x^2+y^2)/2)}{2\pi}dxdy?$$

I think I should make the substitution $u=x^2+y^2$, but I don't know how the integral will look like.

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    This is a Gaussian integral; a recommended method is to use polar coordinates.2012-04-19
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    The word "solve", like one or two others, gets used as a catch-all by non-mathematicians. The right term here is "evaluate". On solves problems; one solves equations; one evaluates expressions.2012-04-19
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    In statistical language, if $X$ and $Y$ are independent standard normal random variables, then $X^2+Y^2$ has a $\chi^2$ distribution with 2 degrees of freedom, that is, an exponential distribution with mean 2.2012-04-19

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