Let $\mathbf { F } ( x , y , z ) = - y \mathbf { j } + x \mathbf { j } + e ^ { z ^ { 2 } } \mathbf { k }$ . Evaluate $\iint _ { S } \operatorname { curl } \mathbf { F } \cdot \mathrm { d } \mathbf { S }$ over the surface S given by $z = \sqrt { 1 - x ^ { 2 } - y ^ { 2 } }$ , with downward orientation.
A) $2 \pi$

B)$\pi$
C)$\frac { \pi } { 2 }$
D)$3 \pi$
E) $- 2 \pi$
F) $- \pi$

G)$- \frac { \pi } { 2 }$

H)$- 3 \pi$

Question

Let $\mathbf { F } ( x , y , z ) = - y \mathbf { j } + x \mathbf { j } + e ^ { z ^ { 2 } } \mathbf { k }$ . Evaluate $\iint _ { S } \operatorname { curl } \mathbf { F } \cdot \mathrm { d } \mathbf { S }$ over the surface S given by $z = \sqrt { 1 - x ^ { 2 } - y ^ { 2 } }$ , with downward orientation.
A) $2 \pi$

B)$\pi$ 
C)$\frac { \pi } { 2 }$ 
D)$3 \pi$ 
E) $- 2 \pi$ 
F) $- \pi$

G)$- \frac { \pi } { 2 }$

H)$- 3 \pi$

Quizplus · Accepted Answer

The Answer of Let $\mathbf { F } ( x , y , z ) = - y \mathbf { j } + x \mathbf { j } + e ^ { z ^ { 2 } } \mathbf { k }$ . Evaluate $\iint _ { S } \operatorname { curl } \mathbf { F } \cdot \mathrm { d } \mathbf { S }$ over the surface S given by $z = \sqrt { 1 - x ^ { 2 } - y ^ { 2 } }$ , with downward orientation.
A) $2 \pi$

B)$\pi$ 
C)$\frac { \pi } { 2 }$ 
D)$3 \pi$ 
E) $- 2 \pi$ 
F) $- \pi$

G)$- \frac { \pi } { 2 }$

H)$- 3 \pi$

Let F(x,y,z)=−yj+xj+ez2k\mathbf { F } ( x , y , z ) = - y \mathbf { j } + x \mathbf { j } + e ^ { z ^ { 2 } } \mathbf { k }F(x,y,z)=−yj+xj+ez2k

Let $\mathbf { F } ( x , y , z ) = - y \mathbf { j } + x \mathbf { j } + e ^ { z ^ { 2 } } \mathbf { k }$