I am trying to run the following code

l = N@Subdivide[-1, 1, 20][[;; -2]] + 1/20;
data = Table[NIntegrate[        
     Log[r^2 + (x^2 + y^2) - 2 r*Sqrt[x^2 + y^2]*Cos[t - ArcTan[x, y]]]
    , {t, 0, 2 Pi }, {r, 0, 1/Sqrt[4 Cos[t]^2 + 25 Sin[t]^2]}, 
    PrecisionGoal -> 6], {x, l}, {y, l}];

and I am getting the error

NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small.

The $x$ and $y$ are parameters for the integration. Is is possible to get the values of $x$ and $y$ for which I am getting the error?

  • $\begingroup$ NIntegrate::slwcon is a warning, not an error. If the integral fails to converge, then it's a hint about what might be the problem. If the integral converges, then it can be ignored. (Of course, numerical methods might mess up, that is, give a result that is erroneous without giving any message about it.) $\endgroup$
    – Michael E2
    Commented Jul 16, 2023 at 15:38

1 Answer 1


If you define

int[x_?NumericQ, y_?NumericQ] := 
    r^2 + (x^2 + y^2) - 
     2 r*Sqrt[x^2 + y^2]*Cos[t - ArcTan[x, y]]], {t, 0, 2 Pi}, {r, 0, 
   1/Sqrt[4 Cos[t]^2 + 25 Sin[t]^2]},Method->"LocalAdaptive" ]

Plot3D shows a smooth surface without error message.

Plot3D[int[x, y], {x, -1, 1}, {y, -1, 1}]

enter image description here

Probably case x=0,y=0 causes the message in your solution grid!


Table[{x, y, int[x, y]}, {x, Subdivide[-1, 1, 21]}, {y,Subdivide[-1, 1, 21]}]

which evaluates without error message


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