Suppose we are working in and that we write in the form . Find the volume of the region

for any .

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- Jun 20th 2009, 11:45 AMBruno J.Find the volume of this region!
Suppose we are working in and that we write in the form . Find the volume of the region

for any . - Jun 20th 2009, 12:02 PMMoo
Hello,

__Spoiler__: - Jun 21st 2009, 08:31 AMHallsofIvy
Moo is correct. That volume can be written as the repeated integral

and Moo's answer can be proved by induction on n. - Jun 23rd 2009, 02:24 PMJose27
I don't think it's the simplex, since, for example, in if then the region is unbounded (actually it is an open strip cut at ) and it's area is not finite (Acutally I believe it's only finite if ).

On another note, if I recall correctly a simplex is a set of the form where and where