Re: Integrate and Piecewise

*To*: mathgroup at smc.vnet.net*Subject*: [mg98488] Re: Integrate and Piecewise*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Fri, 10 Apr 2009 04:59:38 -0400 (EDT)*Organization*: Uni Leipzig*References*: <grkglq$6d1$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de

Hi, f3[t_, a_, t0_] := Evaluate[Integrate[f4[tau, a, t0], {tau, -Infinity, t}]] ? Regards Jens Hugh Goyder wrote: > Below I make a piecewise function that is continuous. Then I integrate > it to make another piecewise function. However, the integrated > function is not continuous. Presumable because I do indefinite > integration and each part of the piecewise function needs a constant > of integration. Is there anyway of doing the integration and getting a > continuous function? I would like the function to be zero at minus > infinity. Do I have to break the function out into its parts or can I > keep it all as a Piecewise function? > > Thanks > Hugh Goyder > > f4[t_, a_, t0_] := Piecewise[{ > {0, t - t0 <= -a}, > { 4 (t - t0 + a)/a, -a < t - t0 <= -(3/4) a}, > {1 - 4/a (t - t0 + (3 a)/4), -(3/4) a < t - t0 <= -(1/4) a}, > {-1 + 4/a (t - t0 + a/4), -(1/4) a < t - t0 <= 0}, > {-(4/a) (t - t0 ), 0 < t - t0 <= 1/4 a}, > {-1 + 4/a (t - t0 - 1/4 a), 1/4 a < t - t0 <= 3/4 a}, > {1 - 4/a (t - t0 - 3/4 a), 3/4 a < t - t0 <= a} > }] > > Plot[f4[t, 1, 0], {t, -3, 3}] > > f3[t_, a_, t0_] := Evaluate[Integrate[f4[t, a, t0], t]] > > Plot[f3[t, 1, 0], {t, -3, 3}, PlotRange -> All] >