Re: specifying the integration interval using a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg95835] Re: specifying the integration interval using a function*From*: dh <dh at metrohm.com>*Date*: Wed, 28 Jan 2009 06:32:15 -0500 (EST)*References*: <glmt0r$mqd$1@smc.vnet.net>

Hi, NIntegrate has the Attribute: HoldAll. It does NOT evaluate its arguments. Therefore, to force the argument to be evaluated, you have wrap it into Evaluate: NIntegrate[f[y], Evaluate@Flatten[{y, s[x, D]}]] hope this helps, Daniel pfb wrote: > Hi everybody, > > is it possible to specify the integration interval using a function? > My problem is as follows: > > I have some function f[x] I want to integrate. Actually I want to > obtain a sort of running average, i.e. a > function F[x,D] given by the integral of f[x] over the interval [x-D, x > +D]. > So far, it's easy. I can do that with the following function > > F[x_,D_]:= NIntegrate[f[y],{y,x-D,x+D}] > > However, the function f may have some (integrable) singularities in > the integration interval. > I know that NIntegrate finds it helpful if one tells it the locations > of the singularities. > So I thought: easy! I just need a function s[x,D] whose output is {x- > D, s1,s2,s3, x+D}., > where s1, s2, .. are the singularities of f in the interval. > > I have such a function, but I'm not able to feed it into NIntegrate. > I have tried > > F[x_,D_]:= NIntegrate[f[y],Flatten[{y,s[x,D]}]] > > but mathematica complains that Flatten[{y,s[x,D]}] is not a correct > integration range specification, despite > its evaluation (in a separate cell) gives what I'd expect, i.e. {y,x- > D,s1,s2,s3,x+D}. > > I also tried something like > > r[y_,x_,D_]:=Flatten[{y,s[x,D]}] > > which again gives {y,x-D,s1,s2,s3,x+D}, and then tried > > > F[x_,D_]:= NIntegrate[f[y],r[y,x,D]] > > Mathematica complains also in this case: r[y,x,D] is not a correct > integration range specification. > > In both case it seems that the function providing the integration > range is not evaluated. > Has this anything to do with delayed set (:=)? > > Is there another way of dealing with the intermediate points in an > integration interval? > > Thanks a lot > > F > >

**Re: specifying the integration interval using a function**

**Re: NIntegrate and Plot**

**Re: specifying the integration interval using a function**

**Re: specifying the integration interval using a function**