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

where $F(x,y,z)=4$yzi$-xzj+4e^{xy}k$ and $C$ is the circle $x^2+y^2=16,z=4$ 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

upwards

curlF

The easiest surface to attach to this curve is the disk $x^2+y^{2}16,z=4.$ 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

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

$$