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How to use NIntegrate to integrate a purely numeric vector function?

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  How to use NIntegrate to integrate a purely numeric vector function? andre hollstein <andre.hollstein@googlemail.com> - 2011-05-07 11:33 +0000
    Re: How to use NIntegrate to integrate a purely numeric vector function? Koslicki <koslicki@math.psu.edu> - 2011-05-09 10:22 +0000

#2162 — How to use NIntegrate to integrate a purely numeric vector function?

Hi Mathgroup, I hope you can help me.
I want to use NIntegrate to integrate a purely numeric vector
function. I simplified this problem to an easy example code. In my
application the function f involves some matrix products with an
InterpolatedFunction object (which is a vector)...

So this is my problem:

Clear[f]
f[a_?NumberQ] := {a, a*a} (*f is returning a list*)
NIntegrate[f[a], {a, 2, 3}]

During evaluation of (Local) In[2569]:= NIntegrate::inum: Integrand
f[a] is not numerical at {a} = {2.00796}. >>
During evaluation of (Local) In[2569]:= NIntegrate::inum: Integrand
f[a] is not numerical at {a} = {2.00796}. >>
Out[2571]= NIntegrate[f[a], {a, 2, 3}]

When f returns a scalar it it working just fine:

Clear[f]
f[a_?NumberQ] := a (*f is returning a scalar*)
NIntegrate[f[a], {a, 2, 3}]
Out[2577]= 2.5

There is hopefully a way to solve this issue...

Thanks, Andr=E9

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#2237

Hello,

Since you are integrating a vector-valued function, you simply need to
integrate component-wise. So in your example:

{Integrate[a,{a,2,3}],Integrate[{a*a,{a,2,3}]}

Or more compactly:

Integrate[#,{a,2,3}]&/@{a,a*a}

(Equivalently, replace Integrate[] with NIntegrate[])

Hope this helps,

~David


On May 7, 7:33 am, andre hollstein <andre.hollst...@googlemail.com>
wrote:
> Hi Mathgroup, I hope you can help me.
> I want to use NIntegrate to integrate a purely numeric vector
> function. I simplified this problem to an easy example code. In my
> application the function f involves some matrix products with an
> InterpolatedFunction object (which is a vector)...
>
> So this is my problem:
>
> Clear[f]
> f[a_?NumberQ] := {a, a*a} (*f is returning a list*)
> NIntegrate[f[a], {a, 2, 3}]
>
> During evaluation of (Local) In[2569]:= NIntegrate::inum: Integrand
> f[a] is not numerical at {a} = {2.00796}. >>
> During evaluation of (Local) In[2569]:= NIntegrate::inum: Integrand
> f[a] is not numerical at {a} = {2.00796}. >>
> Out[2571]= NIntegrate[f[a], {a, 2, 3}]
>
> When f returns a scalar it it working just fine:
>
> Clear[f]
> f[a_?NumberQ] := a (*f is returning a scalar*)
> NIntegrate[f[a], {a, 2, 3}]
> Out[2577]= 2.5
>
> There is hopefully a way to solve this issue...
>
> Thanks, Andr=E9

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