       Re: Integrate with piecewise function

• To: mathgroup at smc.vnet.net
• Subject: [mg44068] Re: Integrate with piecewise function
• From: bobhanlon at aol.com (Bob Hanlon)
• Date: Mon, 20 Oct 2003 01:13:37 -0400 (EDT)
• References: <bmt8gd\$87u\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Use a more straightforward definition for dis, i.e., define it using
mathematical functions rather than program control logic

dis[x_,xi_]:=Abs[x-xi];

Integrate[dis[x,0],{x,-1,1/6}]

37/72

Bob Hanlon

In article <bmt8gd\$87u\$1 at smc.vnet.net>, "Chia-Ming"
<yucalf at mail.educities.edu.tw> wrote:

<< 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

```

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