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MathGroup Archive 2009

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Multiple integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg99416] Multiple integral
  • From: Skirmantas Janusonis <janusonis at psych.ucsb.edu>
  • Date: Tue, 5 May 2009 05:42:33 -0400 (EDT)

Can somebody explain this interesting result (below)? 

In: Assuming[a1 > 0 \[And] a2 > 0 \[And] a3 > 0 \[And] a4 > 0, Integrate[Boole[x1^2/a1^2 + x2^2/a2^2 + x3^2/a3^2 + x4^2/a4^2 <= 1], {x1, -a1, a1}, {x2, -a2, a2}, {x3, -a3, a3}, {x4, -a4, a4}]]

Out: 0

The following is correct:

In: Assuming[a1 > 0 \[And] a2 > 0 \[And] a3 > 0, Integrate[Boole[x1^2/a1^2 + x2^2/a2^2 + x3^2/a3^2 <= 1], {x1, -a1, a1}, {x2, -a2, a2}, {x3, -a3, a3}]]

Out: 4/3 a1 a2 a3 \[Pi]

Thanks!


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