The Surface Integral $\int \int$ S $x y z d S \text {, }$

Multiple Choice

The surface integral $\int \int$ S $x y z d S \text {, }$ where S is $z ^ { 2 } = x ^ { 2 } + y ^ { 2 }$ between $z = 1$ and $z = 2$ is

A) $\frac { 5 \sqrt { 5 } - 1 } { 6 }$
B) $\frac { 15 \pi } { \sqrt { 2 } }$
C) $\frac { 17 \sqrt { 17 } - 1 } { 4 }$
D) $\frac { \sqrt { 3 } } { 6 }$
E) 0