Answer
$\approx 44.2$
Work Step by Step
Approximate the double integral with a Riemann sum; to use a nine term sum for this square area $R$, the $x$ and $y$ should have three terms.
$\int\int f(x,y)dA\approx \Sigma _{i=1}^{3}\Sigma _{j=1}^{3}f(x_{i}y_{j}) \triangle A$
Here, $\triangle A =1 \times 1$
$=f(0.5,0.5)+f(0.5,1.5)+f(0.5,2.5)+f(1.5,0.5)+f(1.5,1.5)+f(1.5,2.5)+f(2.5,0.5)+f(2.5,1.5)+f(2.5,2.5)$
$\approx 1.0+2.5+5.5+3.5+4.5+7.0+5.5+6.5+9.0$
$\approx 44.2$
