Answer
$\dfrac{-3}{32}$
Work Step by Step
Consider $\int_{R} f(x,y) dA \approx \dfrac{1}{4} f(\dfrac{-1}{2},0) +\dfrac{1}{8} f(0,0)+\dfrac{1}{8} f(\dfrac{1}{4},0)$
or, $ =\dfrac{-1}{4} (\dfrac{-1}{2})+\dfrac{1}{8} \times (0+\dfrac{1}{4})$
or, $=\dfrac{-3}{32}$
