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NIntegrate and Delayed Functions


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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