Wrong Integral result for a Piecewise function

*To*: mathgroup at smc.vnet.net*Subject*: [mg58545] Wrong Integral result for a Piecewise function*From*: "Dean Nairn" <dnairn at udel.edu>*Date*: Wed, 6 Jul 2005 03:11:32 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

This integral gives gives the wrong result for the interval [2,3] h[x_] := Integrate[Boole[x - 1 < 2 y + 2 z < x], {y, 0, 1}, {z, 0, 1}] Plot[h[x],{x,0,5}] and Plot[Evaluate[h[x]],{x,0,5}] give different plots, The curve should be smooth and bell shaped from 0 to 5, so the first looks correct. The second has a jump discontinuity at 2 and 3. Also h[5/2] and h[x]/.x-> 5/2 give different answers This is using some new features in Mathematica 5.1. Same result on a Mac (10.4) and SunOS (5.9). Breaking into a difference of two integrals gives the correct answer: Integrate[Boole[ 2 y + 2 z < x], {y, 0, 1}, {z, 0, 1}] - Integrate[Boole[ 2 y + 2 z < x-1], {y, 0, 1}, {z, 0, 1}] Finally Integrate[h[x], {x, 0, 5}] and NIntegrate[h[x], {x, 0, 5}] both give the wrong answer, it should be 1. The triple integral is correct Integrate[Boole[x - 1 < 2 y + 2z < x], {y, 0, 1}, {z, 0, 1}, {x, 0, 5}] Any suggestions on integrating over regions with linear constraints? Versions 5.1 has powerful new piecewise functions

**Follow-Ups**:**Re: Wrong Integral result for a Piecewise function***From:*Andrzej Kozlowski <akozlowski@gmail.com>