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. > > >