Use the Divergence Theorem to Calculate the Surface Integral $\iint _ { 5 } \mathbf { F } \cdot d \mathbf { S }$

Multiple Choice

Use the Divergence Theorem to calculate the surface integral $\iint _ { 5 } \mathbf { F } \cdot d \mathbf { S }$ ; that is, calculate the flux of $F$ across $S$ . $\mathbf { F } ( x , y , z ) = x y e ^ { x } \mathbf { i } + x y ^ { 2 } z ^ { 3 } \mathbf { j } - y e ^ { x } \mathbf { k }$ S is the surface of the box bounded by the coordinate planes and the planes $x = 4 , y = 2 \text { and } z = 1$ .

A) $\frac { 11 } { 3 }$
B) $\frac { 5 } { 3 }$
C) $\frac { 1 } { 8 }$
D) $8$
E) $\frac { 7 } { 3 }$