wrong solution for double integral of piecewise function?

*To*: mathgroup at smc.vnet.net*Subject*: [mg96968] wrong solution for double integral of piecewise function?*From*: Tom Roche <tlroche at gmail.com>*Date*: Sat, 28 Feb 2009 06:43:39 -0500 (EST)

wrong solution for double integral of piecewise function I've got a function f[\[Chi]_, \[Psi]_] = {Piecewise[{{k, {a <= \[Chi] <= b, a <= \[Psi] <= b}}}, 0]} I'm attempting to solve for k such that f becomes a probability density function by applying the normalization constraint, i.e. solving for k such that the double (indefinite) integral of f equals 1. I can do this by hand pretty easily, integrating first/inside WRT psi and second/outside WRT chi, and I get (1) k = 1/((b-a)^2) I don't have the world's greatest calculus chops, but that looks correct to me. (Am I missing something?) However, when I use Mathematica to Solve[ First[ Integrate[ Integrate[ f[\[Chi], \[Psi]], {\[Psi], -\[Infinity], \[Infinity]} ], {\[Chi], -\[Infinity], \[Infinity]} ] ] == 1, k ] I get (2) {{k -> -(1/((a - b)^2 (-1 + UnitStep[a - b])))}} which seems wrong to me, though I'll admit I don't know what "UnitStep" means. So I'm wondering * does (1) = (2)? or * have I made a syntax error? or * is this just really hard to solve symbolically? If so, is there a better way to setup this function and its solution?