Which of the following represents the correct formula for the Jacobian determinant when transforming from variables $(x, y)$ to $(u, v)$?
Question 2
If we perform a transformation from $(x, y)$ to $(u, v)$ defined by $u = x - y$ and $v = x + y$, what is the Jacobian determinant of this transformation?
Question 3
Which of the following integrals correctly applies the change of variables formula for a double integral using the Jacobian?
Question 4
What is the geometric interpretation of the absolute value of the Jacobian determinant in a two-dimensional change of variables?
Question 5
Consider the transformation $x = 2u + 3v$, $y = u - v$. What is the value of the Jacobian determinant for this transformation?
