(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 \( u = xy \) $$v = \frac{y}{x}$$.

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