Answer
$ \approx 49.09$
Work Step by Step
The flux through a surface can be defined only when the surface is orientable.
We know that $\iint_S F \cdot dS=\iint_S F \cdot n dS$
Here, $n$ denotes the unit vector.
Since, $\iint_S f(x,y,z) dS \approx \Sigma_{i=1}^n f(\overline(x), \overline(y), \overline(z)) AS_i$
Here, $\iint_S F(x,y,z) dS \approx f(0,2,3) (24)+f(2,2,3) (24)+f(1,0,3) (12) +f(1,4,3) (12) +f(1,2,0) (8)+f(1,2,6) (8) $
$=(24)(e^{-0.5} +e^{-0.7})+(12)(e^{-0.4} +e^{-0.8})+(8)(e^{-0.3} +e^{-0.9})$
$ \approx 49.09$
