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    "Find the area of the region bounded by the curves xy = 1, xy = 4 and the lines y = 2x and y = 4x ( x,y \geq 0 ")

    To find the Jacobian we need the curves in the form of x and y which are in terms of u and v........

    xy = 1, xy = 4 = u

    y/x = 2, y/x = 4 = v

    root(uv) = y......root(u/v) = x......

    Is this right so far?
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    hhhmmm.......seems as though my answer is off by 1.99 after doing all the working, quite possibly I have done that wrong or the answer given is wrong!
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    There's no need to solve for y and x, just find the Jacobian J(x,y) and invert it.
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    (Original post by Glutamic Acid)
    There's no need to solve for y and x, just find the Jacobian J(x,y) and invert it.
    So would it be 4uv/(u^2+v^2)?
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    (Original post by boromir9111)
    So would it be 4uv/(u^2+v^2)?
    u = xy
    v = y/x

    Thus u_x = y, u_y = x
    v_x = -y/x^2, v_y = 1/x

    So J^(-1) = y/x - (-y/x^2*x) = 2y/x = 2v. Thus J = 1/(2v).
 
 
 
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Updated: March 19, 2011
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