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MathGroup Archive 2007

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Re: Re: numeric integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81193] Re: [mg81181] Re: numeric integration
  • From: Vivek Joshi <vivekj at wolfram.com>
  • Date: Sat, 15 Sep 2007 04:10:15 -0400 (EDT)
  • References: <fcb40h$fm3$1@smc.vnet.net> <200709140748.DAA25892@smc.vnet.net>

Alternatively, If you want to make your previous definitions work,  
You could simple change variable x to t for the second integration,

f = NIntegrate[Sin[x + #], {x, 0, 1}] &;

f[0.1]
0.541408

Quiet@NIntegrate[f[t], {t, 0, 0.1}]
0.050097

-Vivek



On Sep 14, 2007, at 2:48 AM, C. Seja wrote:

found two simple solutions:

1) writing

f[y_?NumericQ] := NIntegrate[Sin[x + y], {x, 0, 1}]

instead of

f = NIntegrate[Sin[x + #], {x, 0, 1}] &

2) writing

NIntegrateF[f, {0, 0.1}]

instead of

NIntegrate[f[x], {x, 0, 0.1}]

with the definition

NIntegrateF[f_ , a_] :=
Module[{F},
F[x_?NumericQ] = f[x];
NIntegrate[F[x], {x, a[[1]], a[[2]]}]
];

c. seja


> Hi,
>
> I'd like to intergate a function f with NIntegrate:
> NIntegrate[f[x], {x, 0, 0.1}]
>
> But this doesn't work if, i.e.
>
> f = NIntegrate[Sin[x + #], {x, 0, 1}] &
>
> It will give a wrong result (0.7 instead of 0.05). Why? I mean, I can
> evaluate f at any point without problems, i.e. f[0.1] gives 0.37.  
> So why
> doesn't
>
> NIntegrate[f[x], {x, 0, 0.1}]
>
> work? It doesn't even give a warning! So, is there a proper way to  
> do this
> (without using one two-dimensional NIntegrate)?
>
> Regards
>
> C. Seja
>
>
>



Vivek Joshi
217-372-3454
  vivekj at wolfram.com





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