Re: newbie problem with NIntegrate

*To*: mathgroup at smc.vnet.net*Subject*: [mg49841] Re: newbie problem with NIntegrate*From*: "David W. Cantrell" <DWCantrell at sigmaxi.org>*Date*: Tue, 3 Aug 2004 01:11:13 -0400 (EDT)*References*: <cei8o5$2he$1@smc.vnet.net> <cejs90$cpk$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On Aug. 2, 2004, Garry Helzer wrote: > On Aug 1, 2004, David W. Cantrell wrote: > > "Xiaoxun" <dbjunxiao at hotmail.com> wrote: > >> Hi, all, > >> > >> Please advices: > >> > >> Geom = (200 >=x>= 100 && 50 >= y >= -50 && -20 <= z <= 20); > >> gr[x_, y_, z_] := 2 /; Geom; > >> gr[x_, y_, z_] := 0 /; ! (Geom); > >> N[Integrate[gr[x, y, z], {x, 0, 300}, {y, -100, 100}, {z, -30, 30}] > >> This gives a result of 799995. > >> However, if changing the x range to {x,0,600} results 799993. > >> and {x,0,900} results 0; > >> > >> So what could we do to ensure the right answer? > > > > First, let me note that in problems like this, it's often good to > > write the function using UnitStep. For example, in your problem, it > > can be written as > > > > gr[x_, y_, z_] := 2(UnitStep[x - 100] - UnitStep[x - 200]) > > (UnitStep[y + 50] - UnitStep[y - 50]) > > (UnitStep[z + 20] - UnitStep[z - 20]) > > > > However, doing that in your problem does not happen to be necessary. > > Just get rid of the N[...]. (Did you notice the warning messages you > > were getting?) In other words, the following works fine (regardless of > > whether the upper limit of integration for x is 300, as shown, or 600 > > or 900): > > > > In[1]:= > > Geom = (200 >= x >= 100 && 50 >= y >= -50 && -20 <= z <= 20); > > gr[x_, y_, z_] := 2 /; Geom; gr[x_, y_, z_] := 0 /; ! (Geom); > > Integrate[gr[x, y, z], {x, 0, 300}, {y, -100, 100}, {z, -30, 30}] > > > > Out[1]= > > 800000 > What version are you using? The last expression is returned unevaluated > on my system ( version 5.0.1, Mac OS 10.3.4). The fact that I'm using version 5.0.0 is immaterial. I made a mistake. Sorry! Doing what it _looks_ like I did, the expression is returned unevaluated on my system too. I had actually done the work in the midst of a long session. [The In and Out numbers were really in the thousands.] I had first defined gr in terms of UnitStep, as noted above, and had seen that the symbolic integral worked as desired in several cases. (So far, so good.) I then decided to see if the OP's definition of gr could be used successfully instead. In doing so, I uncritically copied the OP's code, and then deleted the N[]. It seemed to work as desired. What I unfortunately failed to notice was that the OP's code did not in fact change the definition of gr! It was still defined in terms of UnitStep. I apologize for my oversight. Anyway, at least using UnitStep gives an alternative to loading the Calculus`Integration` package and using Boole. David Cantrell

**Re: ListDensityPlot, ColorFunction, and associated confusions**

**Re: Re: newbie problem with NIntegrate**

**Re: Re: newbie problem with NIntegrate**

**The Histogram[] command**