# Thread: Evaluating an integral by change of variables

1. ## Evaluating an integral by change of variables

Q) Evaluate the integral

$

\iint\limits_D (x² - y²)\,dA \\$

$
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 $\frac{1}{2x²-2y²}$

Rewrote the whole thing to find the answer 1.

Is the approach correct?

2. Originally Posted by keysar7
Q) Evaluate the integral

$

\iint\limits_D (x² - y²)\,dA \\$

$
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 $\frac{1}{2x²-2y²}$

Rewrote the whole thing to find the answer 1.

Is the approach correct?