Let $\mathbf { F } ( x , y , z ) = x \mathbf { k }$

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = x \mathbf { k }$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where S is that part of the plane $z = x$ that lies above the square with vertices $( 0,0 ) , ( 1,0 ) , ( 0,1 )$ , and $( 1,1 )$ and has upward orientation.

A) $1$
B) $\sqrt { 2 }$
C) $\sqrt { 3 }$
D) $2$
E) $\frac { \sqrt { 2 } } { 2 }$
F) $\frac { \sqrt { 3 } } { 2 }$
G) $\frac { 1 } { 2 }$
H) $\frac { 1 } { 4 }$