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[2]:= NIntegrate[w^2*1/(s - w), {s, 1, 5}, {w, -5, -1}] Out[2]= 25.8364 You can easily verify this gives the correct value using Integrate. That is using the syntax you attempted to use above: In[3]:= Integrate[w^2*Integrate[1/(s - w), {s, 1, 5}], {w, -5, -1}] Out[3]= -16-84 log(3)+(250 log(5))/3 which is the same result obtained with: In[4]:= Integrate[w^2*1/(s - w), {s, 1, 5}, {w, -5, -1}] Out[4]= -16-84 log(3)+(250 log(5))/3 and In[5]:= %1 // N Out[5]= 25.8364 gives the same result as NIntegrate using the appropriate syntax.