QUESTION $8$

$5-12$ Use Stokes' Theorem to evaluate o$\backslash$int$\_$C F$*$dr$.$

F$($x$,$y$,$z$)=$z$^(2)$i$+2$xj$-$y$^(3)$k;C is the circle x$^(2)+$y$^(2)=1$ in the

xy$-$plane with counterclockwise orientation looking down the

positive z$-$axis.

F$($x$,$y$,$z$)=2$xz$+3$x$^(2)$y$^(2)$j$-6$xyk;C is the rectangle in the plane

z$=$y shown in Figure $15\mathrm{.}8\mathrm{.}2.$

F$($x$,$y$,$z$)=3$zi$+4$xj$+2$yk; C is the boundary of the paraboloid

shown in Figure $15\mathrm{.}8\mathrm{.}3.$

F$($x$,$y$,$z$)=2$zi$+2$xj$-3$y$^(2)$k;C is the triangle with vertices

$(0,0,0),(2,0,2),$ and $(0,2,2)$ and with counterclockwise orien$-$

tation looking down the positive z$-$axis.