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From: g.resta on 5 Feb 2010 03:28
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



From: Leonid Shifrin on 5 Feb 2010 07:13
Hi,

you have a couple of choices. Either use NIntegrate to do both integrations
at once (the domain can
be not necessarily rectangular):

In[1]:= NIntegrate[Cos[x*Sin[t]],{t,0,1},{x,0,2}]

Out[1]= 1.6679

or define your function only on numeric values:

In[2]:= f[x_?NumericQ] := NIntegrate[Cos[x*Sin[t]], {t, 0, 1}];

In[3]:= NIntegrate[f[x], {x, 0, 2}]

Out[3]= 1.6679

Regards,
Leonid


On Fri, Feb 5, 2010 at 11:19 AM, g.resta(a)iit.cnr.it <g.resta(a)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
>
>
>
>


From: DrMajorBob on 5 Feb 2010 07:14
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(a)iit.cnr.it
<g.resta(a)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(a)yahoo.com

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