Re: Integrate with piecewise function

• To: mathgroup at smc.vnet.net
• Subject: [mg44076] Re: [mg44052] Integrate with piecewise function
• From: "Peter Pein" <nospam at spam.no>
• Date: Tue, 21 Oct 2003 02:07:50 -0400 (EDT)
• References: <200310190510.BAA08054@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Chia-Ming,

NIntegrate[] evaluates the integrand for some numeric values of x.
Integrate[] does it's job symbolically. Therefore NIntegrate gets values
from dis[], while Integrate[] gets "Which[...]" unevaluated. If you use
Abs[x-xi] instead of "dis[]", Integrate[] knows how to handle this function.

Integrate[Abs[x],{x,-1,1/6}] gives the desired result.

Peter Pein, Berlin
petsie at arcAND.de
replace && by || to write to me

----- Original Message -----
From: "Chia-Ming" <yucalf at mail.educities.edu.tw>
To: mathgroup at smc.vnet.net
Subject: [mg44076] [mg44052] Integrate with piecewise function

> Excuse me,
>
> I define a function describing the distance on the edge of a circle.
>
> dis[x_, xi_] := Which[ x - xi >= 0, x - xi, x - xi < 0, xi - x]
>
> Then I find that the command Integrate does not yield the result (37/72).
>
> Integrate[dis[x, 0], {x, 0, 1/6}]
>
> If I use the command NIntegrate, only the numerical result is yielded. But
I
> want the
> exact result.
>
> NIntegrate[dis[x, 0], {x, 0, 1/6}]
> 0.513891
>
> How can I get the exact result, just like I keyin the command by hand.
>
> Integrate[-x, {x, -1, 0}] + Integrate[x-0, {x, 0, 1/6}]
> 37/72
>
> Thank you very much for your help!
>
>
> cmyu
>
>

```

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