Math Is Fun Forum

Math1

Member

Registered: 2015-02-06

Posts: 6

Integral Question.

Equation:

The derivative using chain rule:

But, how is the integral determined?

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,441

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.

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).

zetafunc

Moderator

Registered: 2014-05-21

Posts: 2,441

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.

Math1

Member

Registered: 2015-02-06

Posts: 6

Re: Integral Question.

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