Re: numeric integration

*To*: mathgroup at smc.vnet.net*Subject*: [mg81161] Re: [mg81129] numeric integration*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Fri, 14 Sep 2007 03:38:33 -0400 (EDT)*References*: <3216400.1189687710734.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

It works here just fine, although my value f[0.1] doesn't match yours: f = NIntegrate[Sin[x + #], {x, 0, 1}] &; f[0.1] 0.541408 NIntegrate[f[x], {x, 0, 0.1}] 0.0708073 However... there's a subtlety, since that's the wrong integral unless you wanted THIS double integral: Integrate[Sin[x + x], {x, 0, 1}] // N 0.0708073 You probably wanted this one: Integrate[Sin[x + t], {t, 0, 0.1}, {x, 0, 1}] 0.050097 Quiet@NIntegrate[f[t], {t, 0, 0.1}] (NIntegrate::"inumr" errors suppressed by Quiet) 0.050097 Using t as the parameter is different from using x as the parameter, because of the way you defined f. That can be eliminated, along with the NIntegrate::"inumr" errors, by defining f this way: Clear[x, f] f[t_?NumericQ] := NIntegrate[Sin[x + t], {x, 0, 1}] f[0.1] 0.541408 NIntegrate[f[x], {x, 0, 0.1}] 0.050097 NIntegrate[f[t], {t, 0, 0.1}] 0.050097 That's much nicer anyway. Bobby On Thu, 13 Sep 2007 05:29:44 -0500, C. Seja <p5secr2 at uni-jena.de> wrote: > 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 > > > > -- DrMajorBob at bigfoot.com