Evaluate the Surface Integral $\iint _ { S } ( x + y + z ) d S$

Multiple Choice

Evaluate the surface integral $\iint _ { S } ( x + y + z ) d S$ , where S is that part of the plane $z = x$ that lies above the square with vertices $( 0,0 ) , ( 1,0 ) , ( 0,1 )$ , and $( 1,1 )$ .

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