       Re: Piecewise function integrated thrice

• To: mathgroup at smc.vnet.net
• Subject: [mg13983] Re: [mg13942] Piecewise function integrated thrice
• From: BobHanlon at aol.com
• Date: Sat, 12 Sep 1998 16:59:09 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Use the standard package "Calculus`DiracDelta`"

Needs["Calculus`DiracDelta`"];

h[x_]:=UnitStep[x]

Plot[h[x], {x, -1, 3}];

f[x_]:=Integrate[h[t],{t,0,x}];

Plot[f[x], {x, -1, 3}];

g[x_]:=Integrate[f[t],{t,0,x}];

Plot[g[x], {x, -1, 3}];

m[x_]:=Integrate[g[t],{t,0,x}];

Plot[m[x], {x, -1, 3}];

p[x_]:=Integrate[m[t],{t,0,x}];

Plot[p[x], {x, -1, 3}];

Bob Hanlon

In a message dated 9/11/98 6:35:40 PM, dclement at mail.cpod.fr wrote:

>Why can't Mathematica integrate thrice a piecewise defined function?
>Here is what I mean:
>
>This is a step function:
>h[x_]:=If[x>0,1,0]
>It can (of course) be plotted and integrated. Then let:
>f[x_]:=Integrate[h[t],{t,0,x}]
>f, as well as h, can be plotted and if I put
>g[x_]:=Integrate[f[t],{t,0,x}]
>then g can be plotted, but any integral (definite or not) that I attempt
>to compute about g leads to an error message (though g can be
>NIntegrated).

```

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