Let $f ( x , y ) = x ^ { 2 } y$

Multiple Choice

Let $f ( x , y ) = x ^ { 2 } y$ , and let $R = \{ ( x , y ) \mid 0 \leq x \leq 1,0 \leq y \leq 1 \}$ . Let R be its own partition, and let $\left( x _ { 1 } ^ { * } , y _ { 1 } ^ { * } \right)$ be the center of R. Calculate the double Riemann sum of f.

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

B) $\frac { 3 } { 4 }$
C) $\frac { 3 } { 8 }$
D) $\frac { 3 } { 16 }$
E) $\frac { 1 } { 2 }$
F) $\frac { 1 } { 4 }$

G) $\frac { 1 } { 8 }$

H) $\frac { 1 } { 16 }$