- #1

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## Main Question or Discussion Point

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?

- Thread starter wdlang
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- #1

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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?

- #2

tiny-tim

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(try using the X

Show us what you've tried, and where you're stuck, and then we'll know how to help!

- #3

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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!

- #4

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I will try that

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!

i am a physics student, so i am satisfied with a numerical value

so i will also try it with Monte Carlo simulation

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