Re: Integrate with multiple integrals -- bug?

• To: mathgroup at smc.vnet.net
• Subject: [mg67409] Re: Integrate with multiple integrals -- bug?
• Date: Thu, 22 Jun 2006 06:21:36 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```On 6/21/06 at 2:12 AM, ms_usenet at gmx.de (Martin Schoenecker) wrote:

>I am wondering where my or Mathematica's error in reasoning lies:

>In[1]:= Integrate[g[z], {x, 0, a}]
>Out[1]= a*g[z]

>ok, because the function g does not depend on x.

>In[2]:= Integrate[g[z], {z, 0, c}]
>Out[2]= Integrate[g[z], {z, 0, c}]

>ok, function g is not specified at the moment.

>In[3]:= Integrate[g[z], {z, 0, c}, {x, 0, a}]
>Out[3]= Integrate[a*g[z], {z, 0, c}]

>also ok.  Now with the integration order reversed:

>In[4]:= Integrate[g[z], {x, 0, a}, {z, 0, c}]
>Out[4]= a*g[z]

>?? why this result ??

What version of Mathematica are you using. With

In[7]:=
\$Version

Out[7]=
5.2 for Mac OS X (June 20, 2005)

I get

In[6]:=
Integrate[g[z],{z,0,c},{x,0,a}]==Integrate[g[z],{x,0,a},{z,0,c}]

Out[6]=
True

That is, I get the same output as your Out[3] above regardless of the order of integration.
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