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Re: NIntegrate and Delayed Functions
*To*: mathgroup at smc.vnet.net
*Subject*: [mg44150] Re: NIntegrate and Delayed Functions
*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
*Date*: Fri, 24 Oct 2003 04:24:22 -0400 (EDT)
*Organization*: Universitaet Leipzig
*References*: <bn8eov$nkm$1@smc.vnet.net>
*Reply-to*: kuska at informatik.uni-leipzig.de
*Sender*: owner-wri-mathgroup at wolfram.com
Hi,
is
D[Integrate[f[x,t],{t,0,z[x]}],x] not
Integrate[D[f[x,t],x],{t,0,z[x]}] + f[x,z[x]] D[z[x],x]
and should you not restrict the values of G[x] to numeric arguments
with G[x_?NumericQ]:= ...
and should you not use ND[] from NumericalMath`NLimit` ??
Regards
Jens
Mukhtar Bekkali wrote:
>
> Hi all:
>
> I have a function f[x,t] which does not have an explicit integral over t,
> only numerical integral exists. Suppose F[x] is an integral of f[x,t] over
> t where t ranges from 0 to some function r[x]. I need to plot F'[x] or the
> first derivative of F[x] as a function of x (let's call it G[x]). I tried
> to use Integrate but Mathematica cannot handle it for some functional forms
> of f[x,t] so I am trying to use NIntegrate as a delayed function to speed up
> the evaluation. However, I receive an error message that the limit of
> integration cannot be z[x] and an empty graph. Here is the exerpt from my
> code:
>
> G[x_]:=D[NIntegrate[f[x,t],{t,0,z[x]}],x];
> Plot[G[x],{x,0,1}]
>
> What am I doing wrong? Of course all functions,- f[x,t], z[x] have a
> specific form.
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