$(1$ point$)$ Use Stokes' Theorem to evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr$

where $F(x,y,z)=$yzi$-2xzj+2e^{xy}k$ and $C$ is the circle $x^2+y^2=9,z=3$ oriented counterclockwise as viewed from above.

Since the circle is oriented counterclockwise as viewed from above the surface we attach to the circle is oriented $?$

curlF$=$

The easiest surface to attach to this curve is the disk $x^2+y^{2}9,z=3.$ Using this surface in Stokes' Theorem evaluate the following.

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr={\displaystyle \underset{x_1}{\overset{x_2}{}}}{\displaystyle \underset{y_1}{\overset{y_2}{}}}dydx$

where

$y_1$

$y_2=$

$x_1=$

$x_2=$

Evaluate

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr=$