Re: Sort of nested NIntegrate

• To: mathgroup at smc.vnet.net
• Subject: [mg107224] Re: [mg107176] Sort of nested NIntegrate
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Fri, 5 Feb 2010 07:14:14 -0500 (EST)
• References: <201002050819.DAA06471@smc.vnet.net>
• Reply-to: drmajorbob at yahoo.com

```No problem here:

Quit

Clear[fu, f, t]
fu[x_?NumericQ] := NIntegrate[Cos[x*Sin[t]], {t, 0, 1}]

NIntegrate[fu[x]^2, {x, 0, 2}]

1.43171

Plot[fu[x], {x, 0, 2}, PlotRange -> All]

Bobby

On Fri, 05 Feb 2010 02:19:04 -0600, g.resta at iit.cnr.it
<g.resta at iit.cnr.it> wrote:

> I have the following little problem with a function defined by means of
> NIntegrate.
> My function is much more complicated, but the following example suffices.
>
> Suppose I've defined a function in this way
>
> fu[x_] := NIntegrate[ Cos[ x * Sin[t] ],  {t, 0, 1}];
>
> Mathematica can easily compute numerically and plot the function fu.
>
> Now, I want to use the function fu in another NIntegrate, say
>
> NIntegrate[ fu[x]^2, {x,0,2}]
>
> I hoped that was innocuous (maybe slow, since each point of fu require
> another
> automatic quadrature) but I got instead this error:
> NIntegrate::inumr: The integrand Cos[x Sin[t]] has evaluated to non-
> numerical values for all sampling points in the region with boundaries
> {{0,1}}.
>
> I also got a number which looks like the right value, but I'm afraid
> to trust it because
> I do not fully understand the error message. It seems like Mathematica
> is trying to do
> something symbolic with the guts of fu, even if fu is defined by means
> of NIntegrate.
> But I'm probably wrong.
>
> Surely I'm missing something. Can anybody show me the light?
> (that is, the right way to perform similar computations, maybe the
> right option to pass along?)
>
> thank you very much,
> giovanni
>
>
>

--
DrMajorBob at yahoo.com

```

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