Answer
$2 \pi a$
Work Step by Step
We have: $Normal \ Vector ; n=\vec{r_u} \times \vec{r_v}=\cos u i+ \sin u j+0 k$
Now, $F \cdot n = \cos^2 u+\sin^2 u+0=1$
and $\iint_{S} F \cdot N \ d S=\int_{0}^{2 \pi} \int_{0}^{a} (1) \ dv \ du$
or, $= \int_{0}^{2 \pi}[v]_{0}^{a} \ du$
or, $=a \int_{0}^{2 \pi} \ du$
or, $=a [u]_{0}^{2\pi}$
or, $=a (2 \pi-0)$
or, $=2 \pi a$
