Use Stokes's Theorem to Evaluate $\mathbf { F } ( x , y , z ) = x y z \mathbf { i } + y \mathbf { j } + z \mathbf { k } , x ^ { 2 } + y ^ { 2 } \leq 49$

Multiple Choice

Use Stokes's Theorem to evaluate $\mathbf { F } ( x , y , z ) = x y z \mathbf { i } + y \mathbf { j } + z \mathbf { k } , x ^ { 2 } + y ^ { 2 } \leq 49$ and $S$ is the first-octant portion of $z = x ^ { 2 }$ over $x ^ { 2 } + y ^ { 2 } = 49$
Use a computer algebra system to verify your result.

A) $\frac { 16,807 } { 15 }$
B) $- \frac { 16,807 } { 15 }$
C) $- \frac { 33,614 } { 15 }$
D) 0
E) $\frac { 33,614 } { 15 }$