Possible bug in 2D Integration over a Region

*To*: mathgroup at smc.vnet.net*Subject*: [mg131442] Possible bug in 2D Integration over a Region*From*: Peter Fischer <peter.fischer at ziti.uni-heidelberg.de>*Date*: Tue, 23 Jul 2013 17:20:06 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

Hi, I may have identified a bug in Mathematica 8 when doing a 2D integral over a triangular region. Note that I am not an experienced user, so my approach / syntax may be unprofessional.. - I first define a boolean expression describing a triangle in the xy-plane (with varying basewidth 2w). The 3 conditions define the three sides. (This expression is more complicated than it has to be, because of my original problem geometry.) TriangleCondition[w_] = 4 w + 3 y - 6 w y >= 6 x && 4 w + 6 x + 3 y >= 6 w y && w (2 + 6 y) >= 3 y; - I then convert this logical value to 1/0: IsInAcceptance[w_] = Boole[TriangleCondition[w]]; - I want to integrate a 2D parabola in that region, so that the argument of the integrals will be ARG = ({x, y}.{x, y}) * IsInAcceptance[w]; - Now I carry out the integral in 4 different ways, changing only the order and the way I write it down: IntXFIRST = Integrate[ Integrate[ARG, {x, -Infinity, Infinity}], {y, -Infinity, Infinity}] IntYFIRST = Integrate[ Integrate[ARG, {y, -Infinity, Infinity}], {x, -Infinity, Infinity}] IntXY = Integrate[ARG, {x, -Infinity, Infinity}, {y, -Infinity, Infinity}] IntYX = Integrate[ARG, {y, -Infinity, Infinity}, {x, -Infinity, Infinity}] - It turs out that IntYX yields a DIFFERENT result: IntXFIRST == IntYFIRST // Simplify (* yields True *) IntXFIRST == IntXY // Simplify (* yields True *) IntXFIRST == IntYX // Simplify (* yields 2 w <= 1 !!!!!! *) I am using Mathematica Version 8.0.4.0. I had indicated this issue to the Mathematica support, with basically no reaction. There was one mail indicating there may be an issue. In Mathematica 9, the problematic integral just does not evaluate... What do experts think about this? Cheers Peter