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How to calculate the volume of this space

  1. Mar 6, 2010 #1
    in n-dimensional space, there is an area defined by

    \sum_i x_i^4 <1

    what is its volume?
  2. jcsd
  3. Mar 6, 2010 #2


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    Hi wdlang! :smile:

    (try using the X2 and X2 tags just above the Reply box :wink:)

    Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
  4. Mar 9, 2010 #3
    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!
  5. Mar 9, 2010 #4
    I will try that

    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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