# Integrate gives wrong result?

Computing the integral of the Euclidian distance of two points in a plane, Mathematica seems to give a wrong result. This is a simple integral that should not be tricky and can easily be computed by hand. I wonder if this is a bug (and should be reported?), or whether there is something profound to say about this?

Ps. this is with Mathematica 11.

• Please post copy-pastable code, not screenshot. Commented Nov 23, 2016 at 16:51
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– user9660
Commented Nov 23, 2016 at 16:54
• Don't you get an error with NIntegrate, before having the result? Commented Nov 23, 2016 at 16:58
• Strange, on MMA 11.0.0.0 (Ubuntu 16.04) I get 1/15 (2 + Sqrt[2] + 5 ArcSinh[1]) for the first one (without the 10Pi/15) which gives 0.51405 and an error with NIntegrate when no Method is specified. Note that NIntegrate[ Sqrt[(x - a)^2 + (y - b)^2], {x, 0, 1}, {a, 0, 1}, {y, 0, 1}, {b, 0, 1}, PrecisionGoal -> 6, Method -> {"GlobalAdaptive", "MaxErrorIncreases" -> 10000}] gives 0.521405, with an error however. Commented Nov 23, 2016 at 17:02
• I can confirm anderstood's observation. (except that he/she forgot a 2 in the value specified ;D ). "11.0.0 for Microsoft Windows (64-bit)". (Edit: LocalAdaptive as a method works without errors. [a little deviation in the accuracy though]) Commented Nov 23, 2016 at 17:10