Re: Problem finding integral of exponentials
- To: mathgroup at smc.vnet.net
- Subject: [mg59639] Re: [mg59627] Problem finding integral of exponentials
- From: Curtis Osterhoudt <gardyloo at mail.wsu.edu>
- Date: Mon, 15 Aug 2005 06:50:31 -0400 (EDT)
- References: <200508130726.DAA00918@smc.vnet.net> <200508140838.EAA13021@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi, Kevin,
On Mathematica 5.1, I'm having, I presume, about the same problems
you are:
In[49]:=
thisLayer = Assuming[{a > 0, r > 0, totalR > 0, r0 > 0, t > 0, \[Tau] >
0}, Integrate[2*Pi*(1 - r*Exp[(-(t/\[Tau]))*(r0/r)^6]), {r, a, totalR}]]
Out[49]=
(1/3)*Pi*(-6*a + 6*totalR + a^2*ExpIntegralE[4/3, (r0^6*t)/(a^6*\[Tau])]
- totalR^2*ExpIntegralE[4/3, (r0^6*t)/(totalR^6*\[Tau])])
In[50]:=
otherLayer = Assuming[{a > 0, r > 0, totalR > 0, r0 > 0, t > 0, \[Tau] >
0, h > 0}, Integrate[2*Pi*(1 - r*Exp[(-t/\[Tau])*(r0/r)^6]), {r, h,
totalR}]]
Out[50]=
(1/3)*Pi*(-6*h + 6*totalR + h^2*ExpIntegralE[4/3, (r0^6*t)/(h^6*\[Tau])]
- totalR^2*ExpIntegralE[4/3, (r0^6*t)/(totalR^6*\[Tau])])
So thisLayer and otherLayer seem to evaluate OK, but Mathematica gets
stuck on eCont, even if I assume some values for the exponential decay
time and some of the other parameters, and Mathematica can't do
In[87]:=
Integrate[Exp[-ExpIntegralE[4/3, t]], t]
Out[87]=
Integrate[E^(-ExpIntegralE[4/3, t]), t]
- References:
- Using the VectorCalculus
- From: "Eckhard Schlemm" <e.schlemm@t-online.de>
- Problem finding integral of exponentials
- From: Kevin Towles <kbt22@drexel.edu>
- Using the VectorCalculus