Evaluate the Following $\iiint _ { R } x ^ { 2 } y \sin ( z y ) d V$

Multiple Choice

Evaluate the following $\iiint _ { R } x ^ { 2 } y \sin ( z y ) d V$ , where $R = \left\{ ( x , y , z ) : 0 \leq x \leq 1,0 \leq y \leq 2 , \text { and } 0 \leq z \leq \frac { \pi } { 2 } \right\}$

A) $\frac { 1 } { 2 }$
B) $\frac { 3 } { 4 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 1 } { 8 }$