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