Answer
$\dfrac{3 \ln 2}{2}$
Work Step by Step
Consider:
$I= \iint_{R} f(x,y) dA$
or, $= \int_{1}^{2} \int_{x}^{2x} xy^{-1} dy dx$
or, $= \int_{1}^{2}[x \ln (y) ]_x^{2x}$
or, $=\int_{1}^{2} x \ln (2x)- x \ln x dx$
Thus, we have $I=\int_1^{2} \ln 2 x dx=\dfrac{3 \ln 2}{2}$
