Re: is this integration possible with mathematica?

*Subject*: [mg3106] Re: is this integration possible with mathematica?*From*: Sascha at sunmail.lrz-muenchen.de, Unzicker at lrz.uni-muenchen.de*Date*: 2 Feb 1996 04:23:18 -0600*Approved*: usenet@wri.com*Distribution*: local*Newsgroups*: wri.mathgroup*Organization*: Universitaet Muenchen (Germany)*Sender*: daemon at wri.com

md88-msa at nada.kth.se (Mickael Salabasis) writes: >i have encountered a problem in statistics that i cannot seem >to solve without help. >i have a line separating the xy-plane. the line is given by the >following equation: >f(x,y) : f1(x,y)/f2(x,y) = 1 >where >f1(x,y) = exp[-k* ((x-m11)^2 + (y-m12)^2)] + exp[-k*((x-m21)^2 + (y-m22)^2)] >f2(x,y) = exp[-k* ((x-m31)^2 + (y-m32)^2)] + exp[-k*((x-m41)^2 + (y-m42)^2)] >the m's and k are known constants >now i want to calculate the (double) integral of f1 in the area ABOVE the >line defined by f and respectively the integral of f2 for the area BELOWE >the same line. but i have problems with one of the integrals limits as the >function f cannot be manipulated to give an expression of the type y=h(x)... >can it be done and if so how? >any help appreciated preferrably by email >with best regards >majk I think I had a similar problem. You should define a function which takes only 0 and 1 as values: def[x_,y_]:=If[x<y && y>-x,1,0]; And now use NIntegrate: gr10; NIntegrate[Exp[-x^2-y^2] def[x,y],{x,-gr,0,gr}, {y,-gr,gr},SingularityDepth->6,MaxRecursion->6,MinRecursion->0, GaussPoints->100]//Timing You see, I set some options, because it is still fragile! If somebody has a good solution, I would be interested as well! Regards, Alexander Unzicker sascha at space.imp.med.uni-muenchen.de