Re: Nested numerical integration

• To: mathgroup at smc.vnet.net
• Subject: [mg99158] Re: [mg99138] Nested numerical integration
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 29 Apr 2009 03:47:39 -0400 (EDT)
• Reply-to: hanlonr at cox.net

```\$Version

6.0 for Mac OS X PowerPC (32-bit) (June 19, 2007)

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

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

% // N

25.8364

f[w_] = Assuming[{w <= 1}, Integrate[1/(s - w), {s, 1, 5}]]

log((w-5)/(w-1))

Plot[w^2*f[w], {w, -5, -1}]

Visually, the integral is roughly 12*4/2 = 24

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

25.8364

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

25.83639373697124 + 0.*I

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

25.83639378805382 + 0.*I

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

25.8364

fn[w_?NumericQ] := NIntegrate[1/(s - w), {s, 1, 5}];

NIntegrate[w^2*fn[w], {w, -5, -1}]

25.8364

Off[NIntegrate::inumr]

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

25.8364

Bob Hanlon

On Tue, Apr 28, 2009 at 9:51 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?

```

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