       Re: Why is this integral hard for mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg92853] Re: Why is this integral hard for mathematica?
• From: dh <dh at metrohm.ch>
• Date: Wed, 15 Oct 2008 05:37:31 -0400 (EDT)
• References: <gcn466\$710\$1@smc.vnet.net>

```
Hi Kristian,

the anti-derivative has branch cuts. In this case you must figure what

branch you have to take. I guess that this is what Mathematica does.

E.g. set h=0.5;k=1;alpha=1 and integrate from 0 to 1

evaluate the integral and you get: 2.216..

now calculate the anti-derivative at 1 and 0 and take the difference,

you get: -1.537.. , this is wrong

Daniel

Kristian Schmidt wrote:

> Hello

>

> Consider this indefinite integral: Integrate[Sqrt[

>  4 k (1 + \[Alpha] (-1 + \[Epsilon])) + (h + \[Epsilon] -

>     h \[Epsilon])^2], \[Epsilon]]

>

> This evaluates fine. Now try the same integral with limits of 1/2 and 3/2:

> Integrate[Sqrt[

>  4 k (1 + \[Alpha] (-1 + \[Epsilon])) + (h + \[Epsilon] -

>     h \[Epsilon])^2], {\[Epsilon], 1/2, 3/2}]

>

> This hangs, and I haven't been patient enough to wait it out yet :)

>

> k and alpha are just real numbers, and 0<= h <= 1. Adding these assumptions didn't seem to help though.

>

> I cannot see why it hangs. If mathematica is able to compute the antiderivative just fine, isn't it just a matter of substracting the antiderivative with itself in the two limits?

>

--

Daniel Huber

Metrohm Ltd.

Oberdorfstr. 68

CH-9100 Herisau

Tel. +41 71 353 8585, Fax +41 71 353 8907

E-Mail:<mailto:dh at metrohm.com>

Internet:<http://www.metrohm.com>

```

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