Re: Integrate[], Sort[] and Hold[]

*To*: mathgroup at smc.vnet.net*Subject*: [mg101021] Re: [mg100994] Integrate[], Sort[] and Hold[]*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Sun, 21 Jun 2009 07:05:10 -0400 (EDT)*References*: <200906200047.UAA00917@smc.vnet.net>*Reply-to*: drmajorbob at bigfoot.com

Try this: Clear[f, g] f[a_] := Min[2^a, 3^a] g[a_] := Max[2^a, 3^a] Integrate[{f@a, g@a}, {a, -1, 1}] N@% {(2 Log[2] + Log[27])/(Log[2] Log[27]), (Log[3] + 2 Log[4])/( Log[3] Log[4])} {2.04952, 2.54183} NIntegrate[{f@a, g@a}, {a, -1, 1}] {2.04952, 2.54183} Bobby On Fri, 19 Jun 2009 19:47:57 -0500, Neil Stewart <neil.stewart at warwick.ac.uk> wrote: > I am having trouble integrating a function which contains Sort[]. Here > is a > stripped down (if slightly odd) example: > > In = Integrate[Sort[{2, 3}^a], {a, -1, 1}] > Out = {3/Log[4], 8/Log[27]} > > Mathematica is evaluating this as follows. First, Sort[{2, 3}^a] is > evaluated as {2^a, 3^a}. Then Integrate[2^a, {a, -1, 1}] gives the first > term 3/Log[4]. Finally Integrate[3^a, {a, -1, 1}] gives the second term > 8/Log[27]. Note here that Sort[] is sorting 2^a and 3^a without knowing > the > value of a. That is, sort is sorting the raw symbolic expressions. > > I would prefer Sort[] to wait until it knows the value of a before > sorting. > For example, when a is -1, then 2^a = 1/2 and 3^a = 1/3, so Sort[{2, > 3}^a] > would be {1/3, 1/2}. However when a is 1, then 2^a = 2 and 3^a = 3, so > Sort[{2, 3}^a] would be {2, 3}. That is, in the first case the terms are > swapped, but in the second case they are not. So what I'm after is > > In = Integrate[Sort[{2, 3}^a], {a, -1, 1}] > Out = {2/Log[3] + 1/Log[4], 1/Log[2] + 2/Log[27]} > (* This does not actually happen *) > > [If you prefer to picture this, Plot[{2^a, 3^a}, {a, -1, 1}] draws two > increasing lines that cross at a = 0. Mathematica is integrating under > each > curve. I'm trying to integrate under the line made from the two lower > segments, and under the line made from the two upper segments.] > > I've tried using Hold[], ReleaseHold[], and Evaluate[] but have got > myself > into a terrible mess. Obviously with this trivial example I could just > split > the integral up myself, but is there a way to achieve delaying Sort[] > until > a is known? I would be very grateful for any comments. > > > > > -- DrMajorBob at bigfoot.com

**References**:**Integrate[], Sort[] and Hold[]***From:*Neil Stewart <neil.stewart@warwick.ac.uk>