Calculate the Double Riemann Sum of F for the Partition $\left( x _ { i j } ^ { * } , y _ { i j } ^ { * } \right)$

Short Answer

Calculate the double Riemann sum of f for the partition of R given by the indicated lines and the given choice of $\left( x _ { i j } ^ { * } , y _ { i j } ^ { * } \right)$ . $f ( x , y ) = 2 x + x ^ { 2 } y$ , $R = \{ ( x , y ) \mid - 2 \leq x \leq 2 , - 1 \leq y \leq 1 \}$ , $x = - 1$ , $x = 0$ , $x = 1$ , $y = - \frac { 1 } { 2 }$ , $y = 0$ , $y = \frac { 1 } { 2 }$ ; $\left( x _ { i j } ^ { * } , y _ { i j } ^ { * } \right)$ = lower left corner of Rij.