       Re: Integration Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg102032] Re: Integration Problem
• From: Alois Steindl <asteindl at mch2ws4.mechanik.tuwien.ac.at>
• Date: Mon, 27 Jul 2009 05:54:48 -0400 (EDT)
• References: <h4h1vg\$ibr\$1@smc.vnet.net>

```On 07/26/2009 09:52 AM, JerrySpock wrote:
> Hello, everyone.
>
> I'm having a problem integrating to find an arc length.
>
> I have two parametric equations:
>
> x=e^(2t)
>
> and
>
> y=e^(1.5t)
>
> I'm looking for the arc length from 1 to 2.
>
> N[
> Integrate[
> Sqrt[
> (2Exp[2*m])^2 + (1.5Exp[1.5*m])^2
> ],{m, 1, 2}]]
>
> I keep getting the answer 79.6, but my TI-83 says the answer is 49.8.  I've been playing with this for hours, and I can't get it to work.  Any ideas what I'm doing wrong?
>
>      [Edited by: admin on Jul 25, 2009 7:22 AM]
>
Hello,
that is a strange problem; I guess it has to do with branch cutting, bit
I don't understand, why.
If one replaces 1.5 by 3/2, then the integral is correct.
If I do
fg[y_] = Sqrt[(2 Exp[2*y])^2 + (1.5*Exp[1.5*y])^2]
ig[m_] = Integrate[fg[m], m]
then
N[ig-ig]