- #1
wdlang
- 307
- 0
in n-dimensional space, there is an area defined by
\sum_i x_i^4 <1
what is its volume?
\sum_i x_i^4 <1
what is its volume?
Hi all!
I would suggest you give it a try using the transformation formula!
The following maps could be helpful:
[tex]R^n\rightarrow R^n_{\geq 0}\rightarrow B^n[/tex], where B^n is the unit ball.
[tex](x_1,...,x_n)\rightarrow (x_1^2,...,x_n^2):=(y_1,...,y_n)\rightarrow ||y||_2^2=\displaystyle\sum_{k=1}^n y_k^2=\displaystyle\sum_{k=1}^n x_k^4[/tex]
Good luck!