       Re: Nested numerical integration

• To: mathgroup at smc.vnet.net
• Subject: [mg99156] Re: Nested numerical integration
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Wed, 29 Apr 2009 03:47:16 -0400 (EDT)

```On 4/28/09 at 4:45 AM, 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?

It gives you an error since the inner integral won't yield a
numerical value since as far as it is concerned w is undefined.
The way to do this is to use more appropriate syntax as shown in
the second example when you look up NIntegrate in the
Documentation Center. That is:

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

Out= 25.8364

You can easily verify this gives the correct value using
Integrate. That is using the syntax you attempted to use above:

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

Out= -16-84 log(3)+(250 log(5))/3

which is the same result obtained with:

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

Out= -16-84 log(3)+(250 log(5))/3

and

In:= %1 // N

Out= 25.8364

gives the same result as NIntegrate using the appropriate syntax.

```

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