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ya it's cool.you try to find the square of the quantity,with one variable x and the other y.then you integrate them simultaneously,a double integral.It's easy to evaluate once you transform it to polar coordinates.Nice One.Answer is root pi

As our function is an even function therefore split the limit of integration from -infinity to +infinity as 2 times 0 to infinity and use Gamma function by making a suitable substitution. It can also be done by converting the problem into polar form.

Although $\int e^{-x^2}\,dx$ can't be expressed in terms of elementary functions, we can evaluate $\int_{-\infty}^{+\infty} e^{-x^2}\,dx$. Doing so yields $\sqrt{\pi}$ (for justification see http://en.wikipedia.org/wiki/Gaussian_integral#Computation).

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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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TopNewestya it's cool.you try to find the square of the quantity,with one variable x and the other y.then you integrate them simultaneously,a double integral.It's easy to evaluate once you transform it to polar coordinates.Nice One.Answer is root pi

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lower limit is negative infinity..

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is it 0

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You can also look up this pdf

www.stankova.net/statistics.2012/doubleintegration.pdfLog in to reply

another not-so-cool way is to use gamma function.use the substitution x=root u

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squareroot of Pi ? ( Error Function)

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As our function is an even function therefore split the limit of integration from -infinity to +infinity as 2 times 0 to infinity and use Gamma function by making a suitable substitution. It can also be done by converting the problem into polar form.

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This function is not integrable using the methods we learn till Undergraduate college level. I don't know about what we learn in college...

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Although $\int e^{-x^2}\,dx$ can't be expressed in terms of elementary functions, we can evaluate $\int_{-\infty}^{+\infty} e^{-x^2}\,dx$. Doing so yields $\sqrt{\pi}$ (for justification see http://en.wikipedia.org/wiki/Gaussian_integral#Computation).

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It can be solved by GAMMA FUNCTION=integrate(0-infinity)e^-x.x^(n-1)dx for all x>=1 x belongs to Z+!!!

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I think ans is 0 .. I think we can solve it using integration by part

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