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#1 2015-02-17 20:42:57

Math1
Member
Registered: 2015-02-06
Posts: 6

Integral Question.

Equation:

The derivative using chain rule:





But, how is the integral determined?

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#2 2015-02-17 21:25:55

zetafunc
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Registered: 2014-05-21
Posts: 2,432
Website

Re: Integral Question.

That integral is not expressible in terms of elementary functions. That integral evaluates to:

i.e. the imaginary error function, which you can read about here. There are, however, alternative ways of expressing that integral in terms of an infinite series.

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#3 2015-02-19 23:35:18

Math1
Member
Registered: 2015-02-06
Posts: 6

Re: Integral Question.

The imaginary error function described in the link above: Wikipedia - Error function

States:
-------
In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion.
-------

The equation:


is a parabola (and not sigmoid shape).  This can be seen by inputting e^x^2 into the Math is Fun Plotter.  GeoGebra also plots the equation as a parabola with axis of symmetry (x=0) and vertex (1,1).

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#4 2015-02-20 03:18:50

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,432
Website

Re: Integral Question.

I'm not sure what you're getting at. The error function and e^(x^2) are not the same function.

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#5 2015-02-20 18:34:49

Math1
Member
Registered: 2015-02-06
Posts: 6

Re: Integral Question.

Thanks,
Found more information here: YouTube - Integral of exp(-x^2)

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