Answer
$4$
Work Step by Step
Here, we have $\iint_S F \cdot n dS=\iint_D [2 (u^2-v^2)] dA$
or, $=(2) \times \int_{0}^{1} \int_0^{2} 2 (u^2-v^2) du dv$
or, $=(2) \times \int_{0}^{1} [\dfrac{u^3}{3}-uv^2]_0^2 dv$
or, $=(2) \times [\int_{0}^{1} \dfrac{8}{3}-2v^2 dv]$
or, $=2[\dfrac{8}{3}-\dfrac{2}{3}]$
Hence, we have $Flux=4$
