Use the Given Transformation to Evaluate the Integral $\iint _ { R } x y d A$

Short Answer

Use the given transformation to evaluate the integral.
$\iint _ { R } x y d A$ , where $R$ is the region in the first quadrant bounded by the lines $y = x , y = 3 x$ and the hyperbolas $x y = 2 , x y = 4 ; x = \frac { u } { v } , y = v$ .