1. Aug 31, 2012 #1

   unscientific

   

   1. The problem statement, all variables and given/known data
   
   
   The question is attached in the picture.
   
   3. The attempt at a solution
   
   Since V₀ = 1,
   
   Thus V₁ = [itex]\stackrel{1}{2}[/itex]∏R² which is a constant.
   
   Then shouldn't V_n be as in the picture?

    

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   unscientific, Aug 31, 2012
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3. Aug 31, 2012 #2

   Sourabh N

   

   I think there is a typo in the question.
   
   [itex](\sqrt{R^2 - x^2})[/itex] should be [itex](\sqrt{R^2 - x^2})^n[/itex]

    

   Sourabh N, Aug 31, 2012
4. Aug 31, 2012 #3

   unscientific

   

   hmm are u sure about that?

    

   unscientific, Aug 31, 2012
5. Aug 31, 2012 #4

   Sourabh N

   

   Yes.

    

   Sourabh N, Aug 31, 2012
6. Aug 31, 2012 #5

   Bacle2

   

   Science Advisor

   This seems to be the formula for the volume of an n-sphere:
   
   http://en.wikipedia.org/wiki/N-sphere

    

   Bacle2, Aug 31, 2012
7. Aug 31, 2012 #6

   Ray Vickson

   

   Science Advisor

   Homework Helper

   [tex] V_1(R) =
   \int_{-R}^R V_0 \left(\sqrt{R^2-x^2} \right) \, dx = \int_{-R}^R \; 1 \, dx = 2R, [/tex]
   etc.
   
   RGV

    

   Ray Vickson, Aug 31, 2012

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