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