Re: Nested numerical integration

• To: mathgroup at smc.vnet.net
• Subject: [mg99192] Re: Nested numerical integration
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Wed, 29 Apr 2009 06:39:07 -0400 (EDT)
• References: <gt6flm\$rtj\$1@smc.vnet.net>

```tsg.moore at googlemail.com wrote:

> Hi, I'd like to compute a nested integral like,
>
> NIntegrate[ w^2 * NIntegrate[1/(s-w), {s, 1, 5}], {w, -5, -1}]
>
> Unfortunately, mathematica gives me an error (NIntegrate::inumr) and
> it also outputs the wrong value. Is there a way to do these types of
> integrals?
>

Mathematica complains, because your inner integral can't be evaluated
numerically because it depends on the parameter w in it.

You can try this:

NIntegrate[w^2/(s - w), {w, -5, -1}, {s, 1, 5}]

Out= 25.8364

This value seems to be correct (and will be given with your input)
because you can integrate symbolically:

Integrate[w^2  Integrate[1/(s - w), {s, 1, 5}], {w, -5, -1}]

Out= -16 - 84 Log[3] + (250 Log[5])/3

%//N

Out= 25.8364

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

```

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