variable change double integral region defined

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I am looking to solve this



$$int xy(x^2+y^2) dx dy$$



over the region region
$R:-3le x^2-y^2 le3, 1le xy le4$



I tried to change the coordinate system from $x$,$y$ to $u$,$v$
with $x^2-y^2=u$ and $xy=v$
$R:-3le u le3, 1le v le4$
but i am unable to express integrand $xy(x^2+y^2)$ especially $x^2+y^2$ in terms of $u$,$v$



I think I am working with the wrong substitution. Can someone suggest a better one?










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    up vote
    0
    down vote

    favorite
    1












    I am looking to solve this



    $$int xy(x^2+y^2) dx dy$$



    over the region region
    $R:-3le x^2-y^2 le3, 1le xy le4$



    I tried to change the coordinate system from $x$,$y$ to $u$,$v$
    with $x^2-y^2=u$ and $xy=v$
    $R:-3le u le3, 1le v le4$
    but i am unable to express integrand $xy(x^2+y^2)$ especially $x^2+y^2$ in terms of $u$,$v$



    I think I am working with the wrong substitution. Can someone suggest a better one?










    share|cite|improve this question

























      up vote
      0
      down vote

      favorite
      1









      up vote
      0
      down vote

      favorite
      1






      1





      I am looking to solve this



      $$int xy(x^2+y^2) dx dy$$



      over the region region
      $R:-3le x^2-y^2 le3, 1le xy le4$



      I tried to change the coordinate system from $x$,$y$ to $u$,$v$
      with $x^2-y^2=u$ and $xy=v$
      $R:-3le u le3, 1le v le4$
      but i am unable to express integrand $xy(x^2+y^2)$ especially $x^2+y^2$ in terms of $u$,$v$



      I think I am working with the wrong substitution. Can someone suggest a better one?










      share|cite|improve this question















      I am looking to solve this



      $$int xy(x^2+y^2) dx dy$$



      over the region region
      $R:-3le x^2-y^2 le3, 1le xy le4$



      I tried to change the coordinate system from $x$,$y$ to $u$,$v$
      with $x^2-y^2=u$ and $xy=v$
      $R:-3le u le3, 1le v le4$
      but i am unable to express integrand $xy(x^2+y^2)$ especially $x^2+y^2$ in terms of $u$,$v$



      I think I am working with the wrong substitution. Can someone suggest a better one?







      integration multivariable-calculus change-of-variable






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      share|cite|improve this question













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      edited Sep 5 at 11:58









      Deepesh Meena

      3,8912825




      3,8912825










      asked Sep 5 at 11:50









      Omen

      13




      13

























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