I have no idea why the volume is 8 in the first octant, I'm fine with the rest. Can anyone explain to me why this is?
2026-04-05 14:18:46.1775398726
How did this number come about in a volume integral?
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Community wiki answer so the question can be marked as answered:
As Brian noted in a comment, the intended meaning is that the volume is $8$ times the volume in the first octant. Needless to say, that's a rather sloppy way to write this.