RE: Integration of "Which" function

*To*: mathgroup at smc.vnet.net*Subject*: [mg32112] RE: [mg32100] Integration of "Which" function*From*: "David Park" <djmp at earthlink.net>*Date*: Thu, 27 Dec 2001 03:34:14 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Doron, This is a frequent question on MathGroup, and rightly so, since The Mathematica Book leads users down the garden path of multiple definitions for piecewise functions. While occasionally convenient, this is mostly a relic of earlier versions of Mathematica. So here is the rule: TO DO ANALYTICAL WORK WITH PIECEWISE FUNCTIONS DEFINE THEM WITH UnitStep! Mathematica knows all about UnitStep as a function and can integrate it, differentiate it, plot it and generally do all kinds of things with it. Here is your example somewhat extended. I defined the function to be a square pulse between 1/2 and 1, and integrated and plotted between 0 and 2. f[x_] := 2(UnitStep[x - 1/2] - UnitStep[x - 1]) Plot[f[x], {x, 0, 2}]; F[x_] = Integrate[f[x], x] 2*((-(-1 + x))*UnitStep[-1 + x] + (-(1/2) + x)*UnitStep[-(1/2) + x]) Plot[F[x], {x, 0, 2}]; David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ > From: Doron [mailto:klepachd at yahoo.com] To: mathgroup at smc.vnet.net > > Hello , > I am trying to integrate : > Integrate[Which[0 <= x <= 1/2, 0, 1/2 < x <= 1, 2], {x, 0, 1}] > > Why doesn`t it work ? > Thank you for your help . >