Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where $\mathbf { F } = x \mathbf { i } + y \mathbf { j } + x \mathbf { k }$ and S is the part of the plane $z = 1 - x - y$ in the first octant with downward orientation.
A) $\frac { 1 } { 3 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 1 } { 4 }$
D)$1$
E) $- \frac { 1 } { 3 }$
F)$- \frac { 1 } { 2 }$
G)$- \frac { 1 } { 4 }$
H)$- 1$

Question

Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where $\mathbf { F } = x \mathbf { i } + y \mathbf { j } + x \mathbf { k }$ and S is the part of the plane $z = 1 - x - y$ in the first octant with downward orientation.
A) $\frac { 1 } { 3 }$ 
B) $\frac { 1 } { 2 }$ 
C) $\frac { 1 } { 4 }$ 
D)$1$ 
E) $- \frac { 1 } { 3 }$ 
F)$- \frac { 1 } { 2 }$ 
G)$- \frac { 1 } { 4 }$ 
H)$- 1$

Quizplus · Accepted Answer

The Answer of Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where $\mathbf { F } = x \mathbf { i } + y \mathbf { j } + x \mathbf { k }$ and S is the part of the plane $z = 1 - x - y$ in the first octant with downward orientation.
A) $\frac { 1 } { 3 }$ 
B) $\frac { 1 } { 2 }$ 
C) $\frac { 1 } { 4 }$ 
D)$1$ 
E) $- \frac { 1 } { 3 }$ 
F)$- \frac { 1 } { 2 }$ 
G)$- \frac { 1 } { 4 }$ 
H)$- 1$

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

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