Answer
$$\dfrac{-1}{10}$$
Work Step by Step
$$\iint_{R} f(u,v) dA= \int_{0}^{1} [\dfrac{v^2}{2}-v\sqrt u]_0^{1-u} du\\= \int_{0}^{1 } \dfrac{(1-u)^2}{2}-(1-u) \times \sqrt u ] du \\= (\dfrac{1}{3}) \times \int_{0}^{1 } (1-4x^3-3x+6x^2) dx \\= \dfrac{1}{2}+\dfrac{1}{6}-\dfrac{1}{2}-\dfrac{2}{3}+\dfrac{2}{5} \\=-\dfrac{1}{10}$$
