       Re: Integration Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg102031] Re: [mg102004] Integration Problem
• From: Syd Geraghty <sydgeraghty at me.com>
• Date: Mon, 27 Jul 2009 05:54:37 -0400 (EDT)
• References: <200907260755.DAA18985@smc.vnet.net>

```Hi Jerry,

Try

NIntegrate[Sqrt[(2 Exp[2*m])^2 + (1.5 Exp[1.5*m])^2], {m, 1, 2}]

49.7621

To see what is going wrong with your example try

Integrate[Sqrt[(2 Exp[2*m])^2 + (3/2 Exp[3/2*m])^2], {m, 1, 2}]

1/512 (-128 E^(3/2) Sqrt[9 + 16 E] - 36 Sqrt[E (9 + 16 E)] + (324 E)/
Sqrt[
9 + 16 E^2] + (1728 E^3)/Sqrt[9 + 16 E^2] + (2048 E^5)/Sqrt[9 + 16
E^2] +
81 ArcSinh[(4 Sqrt[E])/3] - 81 ArcSinh[(4 E)/3])

N[%]

49.7621

HTH ... Syd

Syd Geraghty B.Sc, M.Sc.

sydgeraghty at mac.com

Mathematica 7.0.1 for Mac OS X x86 (64 - bit) (18th February 2009)
MacOS X V 10.5.6
MacBook Pro 2.33 GHz Intel Core 2 Duo  2GB RAM

On Jul 26, 2009, at 12:55 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]
>

```

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