Computing the volume of higher dimensional polynomials? (4th, 5th, etc)
So, I'm working on a problem set and I'm asked to "compute the volume of the 4th dimensional unit hypersphere x^2 + y^2 + z^2 + w^2 =1" and then after that it goes on to ask me to do the same for 5th, 6th, and 7th dimensional hyperspheres.
( 5th: x^2 + y^2 + z^2 + w^2 + v^2 =1
6th: x^2 + y^2 + z^2 + w^2 + v^2 + s^2 = 1
7th: x^2 + y^2 + z^2 + w^2 + v^2 + s^2 + t^2 =1 ).
Actually computing the volume of these integrals won't be too hard, since I can use the program Maple, but it's the limits that I'm confused about. What would be the limits to the integrals? How do I figure that out?