Let $\mathbf { F } ( x , y , z ) = x ^ { 2 } \mathbf { i }$

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = x ^ { 2 } \mathbf { i }$ and let S be the boundary surface of the solid $E = \{ ( x , y , z ) \mid 0 \leq x \leq 1,0 \leq y \leq 1,0 \leq z \leq 1 \}$ . Evaluate the surface integral $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ .

A) $0$

B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 3 }$
D)
$\frac { 1 } { 2 }$
E) $\frac { 2 } { 3 }$
F) $\frac { 3 } { 4 }$

G) $1$

H) $\frac { 3 } { 2 }$