$\text { Let } \mathbf { F } ( x , y , z ) = z ^ { 2 } \mathbf { i } + 2 x \mathbf { j } + y ^ { 2 } \mathbf { k } \text { and let } S \text { be the graph of }$ $z = 1 - x ^ { 2 } - y ^ { 2 } , z \geq 0$,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

Question

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The Answer of $\text { Let } \mathbf { F } ( x , y , z ) = z ^ { 2 } \mathbf { i } + 2 x \mathbf { j } + y ^ { 2 } \mathbf { k } \text { and let } S \text { be the graph of }$ $z = 1 - x ^ { 2 } - y ^ { 2 } , z \geq 0$,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

z=1−x2−y2,z≥0z = 1 - x ^ { 2 } - y ^ { 2 } , z \geq 0z=1−x2−y2,z≥0

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