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: Tue, 2 Jan 2007 04:17:19 -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.

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