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# Jacobian problem watch

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

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?
2. 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!
3. There's no need to solve for y and x, just find the Jacobian J(x,y) and invert it.
4. (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)?
5. (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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