Jacobian determinant

Definition:

• Used when making a change of variables when evaluating a multiple integral of a function over a region within its domain

$J(x_1,x_2)=\left|\begin{array}{cc}\frac{\partial g_1}{\partial x_1}& \frac{\partial g_1}{\partial x_2}\\ \frac{\partial g_2}{\partial x_1}& \frac{\partial g_2}{\partial x_2}\end{array}\right|$