Evaluate the Triple Integral $\iiint _ { E } z d V$

Multiple Choice

Evaluate the triple integral $\iiint _ { E } z d V$ , where E is the wedge in the first octant bounded by $y ^ { 2 } + z ^ { 2 } = 1$ , y = x, and the yz-plane.

A) $\frac { 1 } { 4 }$

B) $\frac { 1 } { 8 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 2 } { 3 }$
E) $\frac { 3 } { 4 }$
F) 1
G) $\frac { 5 } { 4 }$

H) $\frac { 4 } { 3 }$