Re: Boole does not work with symbolic limits in Integrate ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg73122] Re: Boole does not work with symbolic limits in Integrate ?*From*: "David W. Cantrell" <DWCantrell at sigmaxi.net>*Date*: Sun, 4 Feb 2007 06:33:10 -0500 (EST)*References*: <eq1ihd$2ug$1@smc.vnet.net>

Mitch Murphy <mitch at mix5.com> wrote: > hey hey > > use of the boole indicator function inside integrate only works for > numerical arguments, symbolic limits of integration just returns the > unevaluated integral. > > simple example ... > > Integrate[2 u Boole[a < u], {u, 0, x}] > > out[] = Integrate[2 u Boole[a < u], {u, 0, x}] > > i would expect ... > > Integrate[2 u , {u, a, x}] > > out[] = x^2 - a^2 If that's what you'd expect, then you made some implicit assumptions. For example, Integrate[2 u Boole[a < u], {u, 0, x}] is not equal to x^2 - a^2 if a < 0 and x > 0. To get what you'd expect from Mathematica, just make your assumptions explicit: In[5]:= Integrate[2 u Boole[a < u], {u, 0, x}, Assumptions->(a > 0 && x > a)] Out[5]= -a^2 + x^2 David > but it does work with numerical limits of integration ... > > Integrate[2 u Boole[a < u], {u, 0, 2}] > > out[] = Piecewise[{{4, a <= 0}, {4 - a^2, 0 < a < 2 }] > > anybody know a trick to make this work ? i've tried a bunch of > variations using evaluate[], logicalexpand[], piecewiseexpand[], > assumptions->x Reals, ..., but nothing works. > > cheers, > Mitch