I have run into a problem with a table of numerical integration results. The code that creates the apparent bug is
re = ImplicitRegion[x^2/4 + y^2 + z^2 == 1.0, {x, y, z}];
v[x0_, y0_] := 1/Sqrt[(x - x0)^2 + (y - y0)^2 + z^2];
Table[NIntegrate[
v[xx, yy], {x, y, z} \[Element]
re], {xx, .85, .95, .1}, {yy, .85, .95, .1}]
For xx=.95 and yy=.85, these values are not passed to the integration routine and the resulting table is
{{16.6953, 16.2125}, {NIntegrate[v[xx, yy], {x, y, z} \[Element] re],
15.8431}}
I do not get a similar error if I do the equivalent integration in cylindrical coordinates
v1[x0_, y0_, \[Theta]_, x_] :=
1/Sqrt[(x - x0)^2 + (r[x] Cos[\[Theta]] - y0)^2 +
r[x]^2 Sin[\[Theta]]^2];
Table[NIntegrate[
v1[xx, yy, \[Theta], x] r[x] Sqrt[1 + (x/2)^2/(4 - x^2)], {x, -2,
2}, {\[Theta], 0,
2 \[Pi]}], {xx, .85, .95, .1}, {yy, .85, .95, .1}]
for which the resulting table is
{{16.6953, 16.2125}, {16.6037, 15.8431}}