Results 1 to 5 of 5

Math Help - jacobian help

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    9

    jacobian help

    I have doubt in one question which asks for to evaluate double integrals and here I need to evaluate the Jacobian matrix first.
    \iint e^(-xy/2) dy dx, given that x=sqrt(v/u) and y=sqrt(uv)
    Bounded by graphs y=x/4, y=2x, y=1/x and y=4/x.
    This is what i did:
    I took u=y/x and v=xy with limits u:[0.25,2] and v: [1,4].
    When I am evaluating the jacobian matrix, m getting 8uv^2/9 as the answer which m incorporating in the equation \iint e^(-v/2). 8uv^2/9 du dv which limits for u and v.
    After all this m not getting the correct result which should be approximately 0.97. Where m I possibly going wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Nov 2009
    Posts
    177
    Your Jacobian does not seem right. I'm getting |J(u,v)|=\frac{1}{2u}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2009
    Posts
    177
    You can determine either J(u,v) or J(x,y) \implies J(u,v)=\frac{1}{J(x,y)}.

    Hint: J(x,y) is easier to determine.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2011
    Posts
    9
    Quote Originally Posted by Mondreus View Post
    You can determine either J(u,v) or J(x,y) \implies J(u,v)=\frac{1}{J(x,y)}.

    Hint: J(x,y) is easier to determine.
    Nice! I am hearing this for the first time.. If you don't mind, can you please elaborate more on this? I didn't clearly get how you determined it.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2011
    Posts
    9
    Quote Originally Posted by Sonia View Post
    Nice! I am hearing this for the first time.. If you don't mind, can you please elaborate more on this? I didn't clearly get how you determined it.
    Oh! now I got it.. the only mistake I was making was that I was integrating u and v values instead of differentiating them.
    Thanks a heap for your time! I really appreciate your efforts!
    God bless
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Jacobian help
    Posted in the Calculus Forum
    Replies: 10
    Last Post: December 13th 2010, 02:26 PM
  2. jacobian
    Posted in the Calculus Forum
    Replies: 0
    Last Post: June 6th 2010, 03:12 PM
  3. The Jacobian
    Posted in the Calculus Forum
    Replies: 7
    Last Post: May 3rd 2010, 01:42 AM
  4. jacobian=f(x,y)
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: February 3rd 2010, 08:37 AM
  5. Jacobian
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: October 21st 2009, 08:54 PM

Search Tags


/mathhelpforum @mathhelpforum