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Re: Integration with non-numeric parameters
*To*: mathgroup at smc.vnet.net
*Subject*: [mg79775] Re: Integration with non-numeric parameters
*From*: dimitris <dimmechan at yahoo.com>
*Date*: Sat, 4 Aug 2007 05:51:43 -0400 (EDT)
*References*: <f8v1cb$ded$1@smc.vnet.net>
On 3 , 13:51, ingramfina... at gmail.com wrote:
> When I use Mathematica to solve the following
> y=x1/(2*sigma^2*t)
>
> Integrate[y, {t, .5, 1}]
>
> I get the following answer:
>
> (0.34657*x1/sigma^2)
>
> OK, so far, so good. It appears that I can generate an answer with a
> non-numeric parameter. Note that I am looking for an answer in terms
> of x1.
>
> But when I try
>
> q=Exp[-(x1-t)^2/2*sigma^2*t]
>
> Integrate[q, {t, .5,1}]
>
> Now Mathematica does not solve this integral, it just repeats the
> command
>
> I am trying to get an expression in terms of x1. Why do I get a
> statement like this instead of an answer? There is something about
> the functional form of the integrand that is causing the problem, I
> just don't know what it is.
>
> Any help you can give me is much appreciated!
Do not mix arbitrary precision numbers with symbolic built in
functions.
Use 1/2 instead of 0.5!
So,
In[43]:=
Clear["Global`*"]
In[44]:=
y = x1/(2*sigma^2*t)
Out[44]=
x1/(2*sigma^2*t)
In[45]:=
Integrate[y, {t, 1/2, 1}]
Out[45]=
(x1*Log[2])/(2*sigma^2)
In[46]:=
q = Exp[(-((x1 - t)^2/2))*sigma^2*t]
Out[46]=
E^((-(1/2))*sigma^2*t*(-t + x1)^2)
In[47]:=
Integrate[q, {t, 1/2, 1}]
Out[47]=
Integrate[E^((-(1/2))*sigma^2*t*(-t + x1)^2), {t, 1/2, 1}]
The latter integral is not a trivial one!
In another CAS,
convert("Integrate[E^((-(1/2))*sigma^2*t*(-t + x1)^2), {t, 1/2,
1}]",FromMma,evaluate);
1
/ 2 2
| sigma t (-t + x1)
| exp(- -------------------) dt
| 2
/
1/2
Again the integral is stated unevaluated.
Dimitris
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