Integrate this integral from 0 to x of e^(-t^2)

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SUMMARY

The integral from 0 to x of e^(-t^2) does not have a simple closed form and is designated as the "error function," represented as erf(x) = (2/√π) ∫₀ˣ e^(-t²) dt. This integral frequently appears in statistics and is also known as the Gaussian integral or probability integral. A closed form expression can be obtained when the limits of integration extend to infinity using polar coordinates. The antiderivative of e^(-x²) cannot be expressed using elementary functions.

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someone please show me how to integrate this
integral from 0 to x of e^(-t^2)
Thanks
 
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Your integral has no simple closed form. However, that particular integral appears often enough to warrant its own special designation - it's call the "error function:"

erf(x) = \frac {2}{\sqrt \pi} \int_0^{x} e^{-t^2} dt
 
Don't you square it. Rename a variable. Then transform to polar co-ords. Then you get left with something along the lines of...

I^2 = 2pi.int^x_0 r.e^(-r^2)dr

which is easy.

Think it's also called the guassian integral or probability integral and must be one of the most common integrals, comes up all the time in stats etc...
 
Only when the limits of integration extend to infinity can we get a closed form expression by using that polar-coordinate trick.

What Tide means is that the antiderivative of e^{-x^2} can't be expressed with elementary functions alone.
 

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