$\text { Use Stokes's Theorem to evaluate } \int _ { C } \overrightarrow { \mathbf { F } } \cdot d \overrightarrow { \mathbf { r } }$

Multiple Choice

$\text { Use Stokes's Theorem to evaluate } \int _ { C } \overrightarrow { \mathbf { F } } \cdot d \overrightarrow { \mathbf { r } }$ Use a computer algebra system to verify your results.
Note: $C$ is oriented counterclockwise as viewed from above.
$\begin{array} { l } \overrightarrow { \mathbf { F } } ( x , y , z ) = x y z \hat { \mathbf { i } } + y \hat { \mathbf { j } } + z \hat { \mathbf { k } } \\S : z = x ^ { 2 } , 0 \leq x \leq 3,0 \leq y \leq 3\end{array}$

A) $- \frac { 243 } { 4 }$
B) $\frac { 243 } { 4 }$
C) $- \frac { 27 } { 4 }$
D) $\frac { 9 } { 4 }$
E) $\frac { 27 } { 4 }$