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

Multiple Choice

$\text { Use Stokes's Theorem to evaluate } \int _ { C } \mathbf { F } \cdot d r \text { where }$ $\mathbf { F } ( x , y , z ) = - \ln \sqrt { x ^ { 2 } + y ^ { 2 } } \mathbf { i } + \arctan \frac { x } { y } \mathbf { j } + \mathbf { k }$ and $S$ is $z = 25 - 2 x - 3 y$ over $r = 2 \sin 2 \theta$ in the first octant. Use a computer algebra system to verify your result.

A) 0
B) $\frac { 4 } { 3 }$
C) $\frac { 14 } { 3 }$
D) 4
E) $\frac { 8 } { 3 }$