Problem $5.$ For each surface $S$ given below:

Find a parametrization $r(u,v)of$ the surface $S.$

Find the set $S^{\text{'}}of$ values $(u,v)$ corresponding $toSu$ and $v$ delr$\frac{}{d}$elu and delr$\frac{}{d}$elv.

Set $upan$ integral $to$ find the area $of$ the surface.

You $do$ not need $todo$ the integral.

$(a)$ The surface $S=\{(x,y,z)in{R}^3|-1x1,0y{x}^2,z=cos(xy)\}.$

$(b)$ The surface $S=\{(x,y,z)in{R}^3|(x-1{)}^2+y^{2}1,z=\sqrt[\phantom{2}]{(x-1{)}^2+y^2}\}.$

Problem $6.$ For the surfaces given above, set $up$ the surface integral $of$ the vector field $F(x,y,z)=$

$-zi+yj.$