$($c$)$ Next we'll work on the set up for the surface integral. Remember the evaluation formula for a vector surface integral:

${}_S$curlF$*dS={}_D$curlF$(r(u,v))*(r_u{r}_v)dvdu$

You'll need to use some scratch paper for the calculations below. Record your results here.

$r(u,v)=,$

$F(x,y,z)=$

$r_u=,$

curlF$=$

$r_v=,$

curlF$(r(u,v))=$

$r_u{r}_v=,$

curlF$(r(u,v))*(r_u{r}_v),$

$$

$$

$$

$($d$)$ Now evaluate the surface integral ${}_D$curlF$(r(u,v))*(r_u{r}_v)dvdu.$

$($e$)$ According to Stokes' Theorem, this tells us that the original vector line integral ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr=$

F y$,$z$,-$x$^2>$ and C is the triangle with vertices $(1,0,0),(0,1,0)$ and $(0,0,1)$