(c) \((10\%)\) \(\iint_{\mathcal{F}}\frac{xy}{\sqrt{1 + x^2y^2}} dA\) , where \(R\) is the region bounded by \(xy = 1\) \(xy = 3\) \(y = x\) \(y = 2x\) by the setting \(u = xy\)

$$v = \frac{y}{x}$$.