Change of Variables & the Jacobian · Challenge problem

Let $R$ be the region $y \ge 0$, $\dfrac{y^2}{4} - 1 \le x \le 1 - \dfrac{y^2}{4}$ (it is bounded by two parabolas). Evaluate $\displaystyle\iint_R \dfrac{dA}{\sqrt{x^2 + y^2}}$.