$(5)$ Let $F=($:$x,y,z$:$)$ be a vector field. Let $E$ be the solid unit ball $x^2+y^2+z^{2}1.$

$($a$)$ Calculate the flux of $F$ across the boundary of $E.$ Assume positive orientation. $($Do not use the divergence theorem$)$

$($b$)$ Now use the divergence theorem to verify that your answer from part $($a$)$ is correct.

$(30$ pts$)$