Chapter 15 - Section 15.9 - Change of Variables in Multiple Integrals - 15.9 Exercise - Page 1060: 1

$-6$

Here, we have $\dfrac{\partial x}{\partial u}=2$ and $\dfrac{\partial x}{\partial v}=1$ Also, $\dfrac{\partial y}{\partial u}=4$ and $\dfrac{\partial y}{\partial v}=-1$ Now, $Jacobian =\begin{vmatrix} 2&1\\4&-1\end{vmatrix}=-2-4=-6$