Given the current density J $=-10^4($sin$(2$x$)$e$^(-2$y$)$a$\_$x $+$ cos$(2$x$)$e$^(-2$y$)$a$\_$y$)$ kA$/$m$^2$:

$($a$)$ find the total current crossing the plane y $=1$ in the a$\_$y direction in

the region $0<$ x $<1,0<$ z $<2.$ Find the total current leaving the region $0<$ x$,$ y $<1,2<$ z $<3$ by: $($b$)$ integrating J$$dS over the surface of the cube; $($c$)$ employing the divergence theorem.