QUESTION $2$

Let $S$ be the upper hemisphere, $z=\sqrt[\phantom{2}]{9-x^2-y^2}$ and $C$ is the boundary curve on $xy-$plane oriented counterclockwise. Verify Stokes' Theorem for vec$(F)(x,y,z)=4$vec$(i)+$xvec$(j)+$vec$(k)$ by evaluating the line integral $o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*vec(dr)$ and the surface integral ${}_S(grad$vec$(F))*vec(n)dS.$

$(13$ marks$)$

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