Jacobian & Area Calculation of R x D Under T(u,v)

[Hashmeer]

Homework Statement

Let D be the image of R = [1; 3] x [1; 4]. under the map
T(u; v) = (u^2/v , v^2/u)

(a) Compute the Jacobian of T.
(b) Compute the area of D.

The Attempt at a Solution

I'm pretty sure I found the Jacobian (I got -2v/u + 2u/v), but I am confused on the next part. How exactly do I find the ranges of u and v since I am not given functions for y and x. Or can I solve the u^2/v and v^2/u for the values in the ranges of x and y to find the ranges for u and v. Thanks for the help.

 

[lanedance]

hmm... i would read this as
$$(u,v) \in R = [1, 3] \cross [1, 4]$$

T then maps from R into D
$$D = T(R)$$
or more explicity
$$(s,t) \in D | (s,t) = T(u,v)$$

note i didn't use x & y as i thought they might be confusing the issue