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MathGroup Archive 2007

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Re: question about Mathematica integration function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79854] Re: question about Mathematica integration function
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Tue, 7 Aug 2007 01:26:11 -0400 (EDT)
  • References: <f96ivj$q15$1@smc.vnet.net>

On 6    , 10:35, ingramfina... at gmail.com wrote:
> I am having trouble integrating the following functions in
> Mathematica.
>
> I have a two functions g and g1, where
>
> g = (x/(sigma*Sqrt[2*Pi*t^3]))*Exp[-(x-mu*t)^2/(2*sigma^2*t)]
>
> and
>
> g1= t*(x/(sigma*Sqrt[2*Pi*t^3]))*Exp[-(x-mu*t)^2/(2*sigma^2*t)]
>
> I assign values for sigma and mu, and then integrate g and g1 with the
> limits of integration =BD and 1; I am trying to get an answer in terms
> of x. If I use the Integrate function, Mathematica does not solve this
> integral, it just restates the integral. If I assign a value for x, it
> can numerically solve the integrals if I use NIntegrate, but this is
> not very useful to me. In other words, I am trying to 'analytically'
> integrate this function.
>
> I realize that I have asked a variation of this question earlier in
> the forum, but I feel that if I explicate just what I am interested
> in, it may be helpful.
>
> Any advice on how to get Mathematica (or any other software) to
> generate the answer?

Mathematica can't get a closed form for your integrals.

In general...
Explanation for such failure can be:

1) No closed form solution exists (for indefinite integrals, this
is the case usually; for definite integrals some times).

2) Mathematica's integrator failed to express the closed
form solution

(

which exists and can be found either by the user-hard!-or by
consulting to-easier!-the well known treatises
in integral tables; see for example here

http://amazon.com/s/ref=nb_ss_gw/105-4601676-4004465?initialSearch=1&url=search-alias%3Dstripbooks&field-keywords=%22tables+of+integrals%22&Go.x=3&Go.y=11

)

in terms of built in functions of Mathematica.
In some cases helping a bit Mathematica might be important.

3) A closed form solution exists but it can be expressed in
terms of special functions which are not implemented in
Mathematica.

Dimitris



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