Q) Evaluate the integral

$\displaystyle

\iint\limits_D (x² - y²)\,dA \\$

$\displaystyle

D = \{(x,y)\lvert 0\leq x²+y²\leq 2, 0\leq xy \leq 1\}

$

A) My approach:

u=x²+y²

v=xy

Found the Jacobian to be $\displaystyle \frac{1}{2x²-2y²}$

Rewrote the whole thing to find the answer 1.

Is the approach correct?

Is my answer correct?