Answer
$$96$$
Work Step by Step
$$\eqalign{
& \int_0^4 {\int_y^{2y} {xy} dxdy} \cr
& {\text{Integrate with respect to }}x \cr
& = \int_0^4 {\left[ {\frac{1}{2}{x^2}y} \right]_y^{2y}dy} \cr
& {\text{Evaluating the limits}} \cr
& = \int_0^4 {\left[ {\frac{1}{2}{{\left( {2y} \right)}^2}y - \frac{1}{2}{{\left( y \right)}^2}y} \right]dy} \cr
& = \int_0^4 {\left[ {2{y^3} - \frac{1}{2}{y^3}} \right]dy} \cr
& = \int_0^4 {\frac{3}{2}{y^3}} dy \cr
& {\text{Integrate}} \cr
& = \left[ {\frac{3}{8}{y^4}} \right]_0^4 \cr
& {\text{Evaluating}} \cr
& = \frac{3}{8}{\left( 4 \right)^4} - 0 \cr
& = 96 \cr} $$
