GATE Mechanical Engineering (ME) 2013 Solved Paper

The following surface integral is to be evaluated over a sphere for the given steady velocity vector field, F = xi + yj + zk defined with respect to a Cartesian coordinate system having i, j, and k as unit base vectors.
$\int \underset{\mathit{s}}{\overset{}{\int }}\frac{1}{4}\left(\mathit{F}.\mathit{n}\right)\mathit{d}\mathit{A}$ , Where S is the sphere, x² + y² + z² = 1 and n is the outward unit normal vector to the sphere. The value of the surface integral is