Fixed in 11.3
I have the following issue, trying to evaluate an integral. Mathematica tells me
Integrate[x^2 (1 + x^2)^(1/2) + y + z, {x, y, z} ∈ Sphere[{0, 0, 0}, 1]]
(* 1/2 π (3 Sqrt[2] - Log[2 (2 + Sqrt[2])]) *)
By the way, it also gives me
Integrate[x^2 (1 + x^2)^(1/2), {x, y, z} ∈ Sphere[{0, 0, 0}, 1]]
(* 1/4 π (6 Sqrt[2] + Log[3 - 2 Sqrt[2]]) *)
And, of course,
Integrate[y + z, {x, y, z} ∈ Sphere[{0, 0, 0}, 1]]
(* 0 *)
You can check that the two results are not equal (they differ by $\frac{3\pi}{8}\log 2$); therefore the linearity of the integral is not respected. How can I explain this fact?
Thank you in advance! This is really puzzling me up.
NIntegrate
which has some other issues instead. $\endgroup$MeshRegions
; mostly for the reason that many features haven't been implemented yet. But this issue is really striking. Would you please be so kind and send a bug report to Wolfram Research? $\endgroup$