Answer
$6-6 \ln (2) $
Work Step by Step
The iterated integral can be calculated as:
$\iint_{D} f(x,y) d A=\int_2^4 \int_{y-1}^{7-y} \dfrac{x}{y^2}dx dy\\=\int_2^4 (\dfrac{x^2}{2y^2})_{y-1}^{7-y} dx \\=\int_2^4 [\dfrac{(7-y)^2}{2y^2}-\dfrac{(y-1)^2}{2y^2}] \ dy \\=\int_2^4 (\dfrac{24}{y^2}-\dfrac{6}{y}] \ dy \\=[\dfrac{-24}{y}-6 \ln y ]_2^4\\=\dfrac{-24}{4}-6 \ln 4 +\dfrac{24}{2}+6 \ln 2 \\=6-6 \ln (2) $
