       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>

```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]
>

```

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