FindRoot[ NIntegrate[...] ...] works but generates "NIntegrate::nlim" limit error message!?
- To: mathgroup at smc.vnet.net
- Subject: [mg72493] FindRoot[ NIntegrate[...] ...] works but generates "NIntegrate::nlim" limit error message!?
- From: "William McHargue" <William at McHargue.Org>
- Date: Wed, 3 Jan 2007 00:46:58 -0500 (EST)
Hello,
I wish to solve for an integration result to equal a given value while
varying the upper limit of the integration. It seems a straightforward
thing to do, and in fact it finds the numerical answer, but it
generates an error message at the beginning of the root solving
operation. I create a function to perform a numerical integration with
a passed upper limit of integration:
In[1]:= integralFunction[upperLimit_] := NIntegrate[x, {x, 0,
upperLimit}]
Then I create a function to find a result of this integration that
equals a supplied value with the upper limit of integration as the
independent variable:
In[2]:= rootOfIntegralFunction[solveForValue_] :=
FindRoot[integralFunction[u] == solveForValue, {u, 1},
EvaluationMonitor :> Print[u]]
(I use the EvaluationMonitor to print the value of "u" as it searches
for the solution.)
When I execute the following I get an error message, yet it finds the
correct result:
In[3]:= rootOfIntegralFunction[12.5]
NIntegrate::nlim : x = u is not a valid limit of integration.
More...
1.
13.
2.2
6.78182
4.3982
5.04117
5.00017
5.
5.
Out[3]= {u->5.}
If anyone has any insight into this behavior please let me know. Thank
you!
Bill.