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Math Help - Proove

  1. #1
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    Proove

    I have been working on this for a long time but with no results Could someone please solve this for me.
    Thanks
    KC
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  2. #2
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    Quote Originally Posted by igodspeed View Post

    I have been working on this for a long time but with no results Could someone please solve this for me.
    Thanks
    KC
    you need to change to the generalized spherical coordinates, i.e. put x_1=r \cos \phi_1, \ x_j=r \sin \phi_1 \sin \phi_2 \cdots \sin \phi_{j-1} \cos \phi_j, \ \ 2 \leq j \leq n-2, and

    x_{n-1}=r \sin \phi_1 \sin \phi_2 \cdots \sin \phi_{n-2} \cos \theta, \ x_n=r \sin \phi_1 \sin \phi_2 \cdots \sin \phi_{n-2} \sin \theta, where 0 \leq \phi_j \leq \pi, \ 0 \leq \theta \leq 2 \pi, and 0 \leq r \leq R.

    now find the Jacobian of this transformation and finally using gamma function your multiple integral would be pretty easy to evaluate.
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  3. #3
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    see we did not learn the method that you are referring to, is there another way to solve it?
    Last edited by igodspeed; May 7th 2009 at 08:11 AM.
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  4. #4
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    Quote Originally Posted by igodspeed View Post

    see we did not learn the method that you are referring to, is there another way to solve it?
    there's also an inductive solution. see here.
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  5. #5
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    Wow !

    I finished this pdf in around 2 hours... That was long (hey I'm still a beginner at creating pdf lol). Tell me if there is any mistake.

    I hope this will help ~

    Prerequisites : Integral and transformation in \mathbb{R}^n, integration by parts, reduction formula for integrals, and being brave
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  6. #6
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    Quote Originally Posted by igodspeed View Post
    I have been working on this for a long time but with no results Could someone please solve this for me.
    Thanks
    KC
    Thread closed due to OP's habit of deleting posts after getting replies.
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