Answer
$30$
Work Step by Step
We have: $g(x,y,z) =y$
We set up the integral and solve the flux of $F$ as follows:
$\iint_{S} F \cdot n \ d \theta =\iint_{R} 2 \ dz \ dx$
or, $=\int_{-1}^{2}\int_2^7 2 \ dz \ dx$
or, $= \int_{-1}^{2} (2 z)_{2}^{7} \ dx$
or, $= \int_{-1}^{2} 2(7-2) \ dx$
or, $=[10x]_{-1}^{2}$
or, $=30$
