 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/undated/prelims/mathematics-iii-resit/2/b/i/solution

\frac{\partial ( u , v )}{\partial ( x , y )} = det (- y / x^{2} 1 1/ x 1) = - \frac{x + y}{x ^{2}} .

The change of variables is defined only for

x \neq = 0

. On the interior of the integration region,

x > 0

and

y > 0

, so this Jacobian determinant is negative and nonzero.

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