Sketch the domain $D$ bounded by $y=x^2,y=\frac{1}{2}{x}^2$ and $y=8x.$ Use a change of variables with the map $x=uv,y=u^2$ to calculate

${}_D{y}^{-1}dxdy$

This is an improper integral since $f(x,y)=y^{-1}$ is undefined at $(0,0),$ but it becomes proper after changing variables.

${}_D{y}^{-1}dxdy=$