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