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Help Improving this integral calculation / solution

• To: mathgroup at smc.vnet.net
• Subject: [mg108044] Help Improving this integral calculation / solution
• From: DOD <dcodea at gmail.com>
• Date: Sun, 7 Mar 2010 04:03:39 -0500 (EST)

I have an integral I need to calculate, with one variable left
symbolic, and then use the result to find a numerical solution to an
equation, and the result of the integration is not giving me what I
need:
------
d = .7;
v = .05;
a = .1;
nk = (a + (1 - a) k v t)/(d + a + (1 - a) k v t);

pg[k_] = Exp[1-k];
gavg = Integrate[k pg[k], {k, 1, \[Infinity]}]; (* This is just 2 *)
result =   1/gavg Integrate[nk k pg[k], {k, 1, \[Infinity]},
Assumptions -> 0 < t < 1];
test = FullSimplify[result]

FindRoot[test == t, {t, .1}]

-----
This code always gives up and stays at the initial guess.  So, I look
at the result of the integration, "result" (or it's simplified
version, test2) and calculated it for various values of t, and it is
always zero.
----
test/.t->{.1,.2,.3}
----
Output:{3.36999*10^66, 0., 0.}
-----

So that's a problem.  If I set t=.3, say, and the beginning, and
calculate the integral, I get 0.160047, which is clearly not zero.
-----
d = .7;
v = .05;
a = .1;
t = .3;
nk = (a + (1 - a) k v t)/(d + a + (1 - a) k v t);

pg[k_] = Exp[1 - k];
gavg =Integrate[k pg[k], {k, 1, \[Infinity]}];(*This is just 2*)

result = 1/gavg Integrate[nk k pg[k], {k, 1, \[Infinity]}]
----
Output=0.160047
-----

 So there is a problem in the Integrate step.  So I want to find a
point where the output of that integral (result), as a function of t,
satisfies result=t.  Is there anyway to do this using built-in
functions?

• Follow-Ups:
  • Re: Help Improving this integral calculation / solution
    • From: danl@wolfram.com
  • Re: Help Improving this integral calculation / solution
    • From: DrMajorBob <btreat1@austin.rr.com>