$z = 1 - x ^ { 2 } - y ^ { 2 } , z \geq 0$

Multiple Choice

$\text { Let } \mathbf { F } ( x , y , z ) = z ^ { 2 } \mathbf { i } + 2 x \mathbf { j } + y ^ { 2 } \mathbf { k } \text { and let } S \text { be the graph of }$ $z = 1 - x ^ { 2 } - y ^ { 2 } , z \geq 0$ ,oriented counterclockwise. Use Stokes's Theorem to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ .

A) 0
B) $2 \pi$
C) $\pi$
D) 1
E) 2