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# Problem with integration

Posted 10 years ago
 Hi !I am triyng to calculate the volume of the intersection of three cylinders of same radius r with their axis perpendicular.I know that the formula is V(r) = 8 ( 2 - sqrt) r^3 ( WolframMathWorld -> Steinmetz Solid).The computation with a numerical value (r = 3) give a correct result (see attachment)But the same computation with no numerical value for r give a wrong result -> 8( 1 - sqrt) r^3Thanks to any help.L. Rogliano Attachments:
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Posted 10 years ago
 This bug appears to be fixed in the development version of Mathematica 10.
Posted 10 years ago
 I work with Matematica V 9.0.1 on a iMac late 2013 with OS X 9.0.3 (Mavericks) and 32 Go.I have sent an email to support@wolfram.com with no significant result.
Posted 10 years ago
 This seems to be a bug in Integrate. You might want to send email to support@wolfram.commy system is V 9.01, windows 7, 64 bitClearAll[x, y, z, r,f];expr = Boole[x^2 + y^2 <= r^2 && y^2 + z^2 <= r^2 && z^2 + x^2 <= r^2];f[value_] := {Integrate[expr, {x, -Infinity, Infinity}, {y, -Infinity, Infinity}, {z, -Infinity, Infinity}] /. r -> value,  NIntegrate[expr /. r -> value, {x, -Infinity, Infinity}, {y, -Infinity, Infinity}, {z, -Infinity, Infinity}]  }nowf(*  {-8 (-27 + 27 Sqrt), 126.5298722} *)N[%](*  {-89.47012947, 126.5298722}  *)