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I came across this in a textbook, it says its as good as impossible to integrate this expression. Ive met a lot of smart guys on here, maybe someone can do it?

[tex]\int exp (-x^2) dx[/tex]

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- Thread starter Kawakaze
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- #1

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I came across this in a textbook, it says its as good as impossible to integrate this expression. Ive met a lot of smart guys on here, maybe someone can do it?

[tex]\int exp (-x^2) dx[/tex]

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tiny-tim

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Hi Kawakaze!

Sorry, the only way is to look it up in tables of erf(x) (the "error function") … see http://en.wikipedia.org/wiki/Error_function" [Broken]

(unless the limits are -∞ to ∞, or 0 to ±∞)

Sorry, the only way is to look it up in tables of erf(x) (the "error function") … see http://en.wikipedia.org/wiki/Error_function" [Broken]

(unless the limits are -∞ to ∞, or 0 to ±∞)

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Gib Z

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[tex]\int e^{-x^2}dx=\sum_{n=0}^{\infty}(-1)^n\frac{x^{2n+1}}{n!(2n+1)}+c[/tex]

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Gib Z

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I

where y is just a dummy variable. Change to polar co-ordinates

r

dxdy=rdrdθ

I

which is trivial to calculate. You then take the square root of the answer.

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I^{2}=∫e^{-x2}∫e^{-y2}

where y is just a dummy variable. Change to polar co-ordinates

r^{2}= x^{2}+y^{2}

dxdy=rdrdθ

I^{2}=∫∫re^{-r2}drdθ

which is trivial to calculate. You then take the square root of the answer.

Right. So you won't mind us giving us the value of

[tex]\int_0^1 e^{-x^2}dx[/tex]

if it is so trivial??

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