Problem $1.(15$ points$).$ Subject: flow rate $($Cartesian coordinates$).$

In $3-$dimensional space, projections of a fluid velocity vector vec$(v)=[v_x,v_y,v_z]$ onto a Cartesian coordinate

system $\{xyz\}$ display the following dependencies

$v_x(x,y,z)(c\frac{m}{m}in)=(si{n}^2(0\mathrm{.}2+0\mathrm{.}3x))cos(0\mathrm{.}5y)e^{-2z}$

$v_y(x,y,z)(c\frac{m}{m}in)=\frac{2z}{ln(1+y)}$

and $v_z(x,y,z)(c\frac{m}{m}in)=x{y}^2(z+0\mathrm{.}5)$

The unit of measurement for $x,y,$ or $z$ is cm $.$ Calculate the volumetric flow rate through a flat $2cm3cm$

rectangular surface defined in space by the following three conditions $(x=1cm,0$