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1

works in 12.3.1 Plot3D[x y, {x, y} \[Element] Disk[{0, 0}, 1], ImageSize -> 500, PlotTheme -> "Web"]


0

Use ImplicitRegion: region = With[{a = 1, b = 1/2, c = 1, d = .03, Ef = .5}, With[{sq = Sqrt[(b - x^2 - y^2)^2 + d (x^2 + y^2)]}, ImplicitRegion[ Abs[a*x - sq] < Ef && Abs[a*x + sq] < Ef, {x, y} ] ] ] (* test it works and we get a point *) RandomPoint[region] (* NIntegrate[f[x,y], {x,y} ∈ region] *)


-1

This is not a general answer. But it works for the problem at hand. Since the integrand is simple enough (a Gaussian) it can be integrated over the variable the analytically. The integral over r is done afterwards numerically, with the default NIntegrate configuration. Clear[PDFTheta] PDFTheta[the_] := PDF[ NormalDistribution [0, DeltaTheta/2], the] theLimUp[...


3

It seems that use Contours and RegionFunction is more effective. f[r_, t_] := 1/2 (Tan[(t - r)/2] + Tan[(t + r)/2]); cond1 = 0 <= r <= Pi && Abs[t] + r < Pi; cond2 = Reduce[cond1, {r, t}]; reg1 = ImplicitRegion[cond1, {r, t}]; Show[RegionPlot[reg1, PlotStyle -> None], ContourPlot[f[r, t], {r, 0, Pi}, {t, -4, 4}, Contours -> {1, -1}, ...


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