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Math Help - Suitable change of variables for this triple integral?

  1. #1
    LHS
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    Suitable change of variables for this triple integral?



    Can anyone help me with coming up with a suitable change of variables for this triple integral? (last part of question)
    having trouble getting spherical polars to work, if anyone has any other suggestions it would be great!

    this is from here, not a take home test
    Course Material for Calculus in Three Dimensions and Applications | Mathematical Institute - University of Oxford
    sheet 3
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Hint Use the Spectral Theorem for the corresponding quadratic form and apply the substitution (x,y,z)^t=P(u,v,w)^t with P orthogonal such that P^{-1}AP=D (D diagonal) .
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  3. #3
    LHS
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    Yeah.. thanks, but as that's not in my first year course the questions i'm facing aren't really geared towards that approach, it would probably be better for me to understand how they want me to do it
    Thanks you though
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by LHS View Post
    Yeah.. thanks, but as that's not in my first year course the questions i'm facing aren't really geared towards that approach, it would probably be better for me to understand how they want me to do it
    Thanks you though

    Haven't you studied a previous Linear Algebra course?
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