Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ where $\mathbf { F } = ( x , y , z ) = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$ and S is the part of the surface $z = 1 - x ^ { 2 } - y ^ { 2 }$ that lies above the $x y -$ plane and has upward orientation.
A) $- 3 \pi$
B) $- \frac { 3 \pi } { 4 }$

C)$- \frac { 3 \pi } { 2 }$
D)$1$
E)$3 \pi$
F)$\frac { 3 \pi } { 4 }$
G) $\frac { 3 \pi } { 2 }$
H)$\frac { 4 \pi } { 3 }$

Question

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ where $\mathbf { F } = ( x , y , z ) = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$ and S is the part of the surface $z = 1 - x ^ { 2 } - y ^ { 2 }$ that lies above the $x y -$ plane and has upward orientation.
A) $- 3 \pi$ 
B) $- \frac { 3 \pi } { 4 }$
 
C)$- \frac { 3 \pi } { 2 }$ 
D)$1$ 
E)$3 \pi$
F)$\frac { 3 \pi } { 4 }$ 
G) $\frac { 3 \pi } { 2 }$ 
H)$\frac { 4 \pi } { 3 }$

Quizplus · Accepted Answer

The Answer of Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ where $\mathbf { F } = ( x , y , z ) = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$ and S is the part of the surface $z = 1 - x ^ { 2 } - y ^ { 2 }$ that lies above the $x y -$ plane and has upward orientation.
A) $- 3 \pi$ 
B) $- \frac { 3 \pi } { 4 }$
 
C)$- \frac { 3 \pi } { 2 }$ 
D)$1$ 
E)$3 \pi$
F)$\frac { 3 \pi } { 4 }$ 
G) $\frac { 3 \pi } { 2 }$ 
H)$\frac { 4 \pi } { 3 }$

Evaluate ∬SF⋅dS\iint _ { S } \mathbf { F } \cdot d \mathbf { S }∬S​F⋅dS

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$