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

Multiple Choice

Use Stokes's Theorem to evaluate $\int _ { C } \mathbf { F } \cdot d r$ where $\mathbf { F } ( x , y , z ) = y z \mathbf { i } + ( 2 - 3 y ) \mathbf { j } + \left( x ^ { 2 } + y ^ { 2 } \right) \mathbf { k } , x ^ { 2 } + y ^ { 2 } \leq 400$ and $S$ is the first-octant portion of $x ^ { 2 } + y ^ { 2 } \leq 400$ over $x ^ { 2 } + y ^ { 2 } = 400$ . Use a computer algebra system to verify your result.

A) $- \frac { 400 } { 3 }$
B) 0
C) $- \frac { 8000 } { 3 }$
D) $\frac { 400 } { 3 }$
E) $\frac { 8000 } { 3 }$