I define a region as follows:

In[259]:= \[ScriptCapitalR] = 
  Polygon[{{0, 0}, {Re[gam2], Im[gam2]}, {gam1 + Re[gam2], 
     Im[gam2]}, {gam1, 0}}] ;

According to http://reference.wolfram.com/language/ref/NIntegrate.html, I should be able to integrate over this region simply as follows:

NIntegrate[x^2 *y^2, {x, y} \[Element] \[ScriptCapitalR]]

But I keep getting this error:

NIntegrate::vars: Integration range specification {x,y}\[Element]\[ScriptCapitalR] is not of the form {x, xmin, ..., xmax}. >>

Why is that?

  • $\begingroup$ Using regions in NIntegrate was introduced in V10. I suspect you're using an earlier version of Mathematica. $\endgroup$
    – Michael E2
    Feb 19, 2015 at 22:12
  • $\begingroup$ Oh my good, you are right! I have V9. $\endgroup$
    – ap21
    Feb 20, 2015 at 8:38

1 Answer 1


Works for me:

gam1 = 2; gam2 = 1 - 2 I;
ℛ = Polygon[{{0, 0}, {Re[gam2], Im[gam2]}, {gam1 + Re[gam2], 
    Im[gam2]}, {gam1, 0}}];

NIntegrate[x^2*y^2, {x, y} ∈ ℛ]

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