Re: Re: Integrate vs NIntegrate

• To: mathgroup at smc.vnet.net
• Subject: [mg47000] Re: Re: Integrate vs NIntegrate
• From: "Mukhtar Bekkali" <mbekkali at iastate.edu>
• Date: Fri, 19 Mar 2004 01:35:53 -0500 (EST)
• Organization: Iowa State University
• References: <c31ca3\$7kk\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Actually, it worked for me in 4.2, but I since upgraded to 5.0 and it does
not now.  I found a workaround though.

"Reza Malek-Madani" <research at usna.edu> wrote in message
news:c31ca3\$7kk\$1 at smc.vnet.net...
> This worked for me on Mathematica 4.2:
>
> f = D[1/(1 + (1 + (a - b)^2)), a];
> h[a_] := NIntegrate[f*b*(1 - b)^2, {b, 0, 1}];
> FindRoot[h[a] == 0, {a, 0, 1}]
>
> Output:
>
> {a -> 0.397861}
>
> Reza
>
>
>
>
> -------------------------------------------------------------------------
> Reza Malek-Madani, Director of Research and Scholarship
> Research Office, MS 10m,   Nimitz Room 17
>
> Annapolis MD 21402-5031
>
> Phone: 410-293-2504 (FAX -2507), DSN: 281-2504
> Email: research at usna.edu
>
> --------------------------------------------------------------------------
> >>> "Curt Fischer" <crf3 at po.cwru.edu> 03/12/04 11:39 PM >>>
> Mukhtar Bekkali wrote:
> > I am confused why NIntegrate misbehaves on such a simple function as
> > mine.
> >
> > Here is what I have:
> >
> > In:
> >
> > f=D[1/(1+(1+(a-b)^2)),a];
> > g=Integrate[f*b*(1-b)^2,{b,0,1},Assumptions->0<a<1];
> > FindRoot[g==0,{a,0,1}]
> >
> > Out:
> >
> > a->0.397207
> >
> > However, since Integrate takes long, I tried to use NIntegrate
> > instead and this is what I get
> >
> > In:
> >
> > f=D[1/(1+(1+(a-b)^2)),a];
> > g:=NIntegrate[f*b*(1-b)^2,{b,0,1}];
> > FindRoot[g==0,{a,0,1}]
> >
> > Out:
> >
> > a->1
> >
> > or, FindRoot+NIntegrate give me the upper boundary of a.  If I
> > abandon the secant method and turn to Newton, i.e. use
> > FindRoot[g==0,{a,0.5}] instead then I get the message that Jacobian is
> > singular at a=0.5 and get no solution.  Perturbing the starting value
> > of a does not help.
> >
> > What is going on here?
>
> My guess is that NIntegrate does not do problems with symbolic
> parameters,
> and yet you are trying to make it calculate the integral of an
> expression
> involving a, with no numerical value for a defined.
>
> --
> Curt Fischer
>
>
>
>
>
>
> > PS.  Is there a way to get M5 to tackle the problem where:
> > (1) I define some function f[x]:=NIntegrate[g[x,y],{y,0,1}], then
> > (2) take the derivative of f[x] with respect to x, say h[x]:=f'[x]
> > and then (3) Use FindRoot to find x such that h[x]==0
>
>

```

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