Nintegrate error: evaluation of function outside integration region

Question

I'm trying to integrate this function with mathematica 9

NIntegrate[
 c4[u, v, w] Cos[ 2*w] , {u, -\[Infinity],
   0}, {v, -\[Infinity], u}, {w, -\[Infinity], v]

with
c4[x_, y_, z_] := 
  E^(-((x^2 + y^2 + z^2)/
    4 )) (E^((x y)/2 ) + E^((x z)/2 ) + E^((y z)/2));

I have this error:

NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after 27 recursive bisections in v near {u,v,w} = {0.0000318293,2.37147*10^-13,0.0000318293}. NIntegrate obtained -6.039603923653673*10^7640189323695 and 6.039603923653673`15.954589770191005*^7640189323695 for the integral and error estimates. >>

NIntegrate tries to evaluate the integrand outside the integration region. How is it possible?

agentp agentp · Accepted Answer · 2013-06-06T20:35:39

I suspect it not, rather NIntegrate is internally making a variable substitution to the posivive domain so that the error message is confusing:

Notice if you do this change yourself you get the exact same error message.

 NIntegrate[c4[-u, -v, -w] Cos[-2 w], {u, 0, \[Infinity]}, {v,  u, \[Infinity]}, {w, v, \[Infinity]}]

If you look what happens with finite bounds:

ListPlot[Table[ {s,
  NIntegrate[
   c4[u, v, w] Cos[2 w],
            {u, -s, 0}, 
             {v, -s, u}, 
             {w, -s, v}]} ,   {s, 1, 8, .25}], Joined -> True]

enter image description here

I think you'll see this thing is not likely to converge at infinity..

Nintegrate error: evaluation of function outside integration region

1 Answers