Re: Integration Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg102042] Re: Integration Problem
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Mon, 27 Jul 2009 05:56:39 -0400 (EDT)
• References: <h4h1vg\$ibr\$1@smc.vnet.net>

```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]
>

Using NIntegrate will give you the result your TI gives

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

Out=49.7621

If you would use Rationals instead of Reals, which is always a good
idea, then Integrate will give you the same result:

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

Out=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[l]   gives  the expected 49.7621

--
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

```

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