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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[2]) 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[2]) r^3

Thanks to any help.

L. Rogliano
Attachments:
POSTED BY: Louis Rogliano
3 Replies
This bug appears to be fixed in the development version of Mathematica 10.
POSTED BY: David Reiss
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 BY: Louis Rogliano
This seems to be a bug in Integrate. You might want to send email to support@wolfram.com
my system is V 9.01, windows 7, 64 bit
ClearAll[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}]
  }
now
f[3]
(*  {-8 (-27 + 27 Sqrt[2]), 126.5298722} *)
N[%]
(*  {-89.47012947, 126.5298722}  *)
POSTED BY: Nasser M. Abbasi
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