       Re: NIntegrate and Delayed Functions

• To: mathgroup at smc.vnet.net
• Subject: [mg44136] Re: NIntegrate and Delayed Functions
• From: "Carl K. Woll" <carlw at u.washington.edu>
• Date: Fri, 24 Oct 2003 04:24:05 -0400 (EDT)
• Organization: University of Washington
• References: <bn8eov\$nkm\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Mukhtar,

As Paul Abbott said in a recent post, use the fundamental theorem of
calculus: For arbitrary function f[x,y], we have

D[Integrate[f[x,t],{t,0,z[x]}],x] ==
Integrate[Derivative[1, 0][f][x, t], {t, 0, z[x]}] + f[x, z[x]] z'[x]

So, we can define your G[x] as

G[x_]:=NIntegrate[Derivative[1, 0][f][x, t], {t, 0, z[x]}] + f[x, z[x]]
z'[x]

Carl Woll

"Mukhtar Bekkali" <mbekkali at hotmail.com> wrote in message
news:bn8eov\$nkm\$1 at smc.vnet.net...
> 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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