Re: Problem finding integral of exponentials
- To: mathgroup at smc.vnet.net
- Subject: [mg59631] Re: [mg59627] Problem finding integral of exponentials
- From: "David Park" <djmp at earthlink.net>
- Date: Mon, 15 Aug 2005 06:50:25 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Kevin,
'=CF=94' is not a valid symbol name, and the others are just substituting
one symbol for another. You want to use Assumptions or Assuming. For the
first integral...
Assuming[Inequality[0, LessEqual, a, Less, TotalR] &&
t > 0 && DonarLifetime > 0 && r0 > 0,
Integrate[(1 - E^(-((t*(r0/r)^6)/DonarLifetime)))*2*
Pi*r, {r, a, TotalR}]]
(1/3)*Pi*(-3*a^2 + 3*TotalR^2 +
a^2*ExpIntegralE[4/3, (r0^6*t)/
(a^6*DonarLifetime)] -
TotalR^2*ExpIntegralE[4/3, (r0^6*t)/
(DonarLifetime*TotalR^6)])
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: Kevin Towles [mailto:kbt22 at drexel.edu]
To: mathgroup at smc.vnet.net
I have a fairly specific problem of not being able to obtain the
definte integral of a fairly complex function. Does this mean that
this integral is not possible in Mathematica?
a = AverageDiameter;
r0 = ForsterRadius;
h = BilayerThickness;
R = DomainDiameter;
=CF=84 = DonorLifetime;
ThisLayer = Integrate[(1 - Exp[(-(t/=CF=84))*(r0/r)^6])*2*Pi*r,
{r,a,TotalR}];
OtherLayer = Integrate[(1 - Exp[(-(t/=CF=84))*(r0/r)^6])*2*Pi*r, {r,
h,TotalR}];
pCont = Exp[-(t/=CF=84)]*Exp[(-=CF=83A)*(ThisLayer + OtherLayer)];
Econt = 1 - (1/=CF=84)*Integrate[pCont, {t, 0, TotalTime}];
All of the variable listed first (a, r0, h, R, and tau) are constants.
Any help is appreciated,
Kevin Towles