vec$(F)=(x+z)vec(i)+$xvec$(j)+$yvec$(k)$ and $Cis$ the upper half $of$ the circle

$x^2+z^2=81in$ the plane $y=0,$ together with the $x-$axis from

$(9,0,0)to(-9,0,0),$ traversed counterclockwise when viewed from

the positive $y-$axis.

Calculate the circulation, ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)in$ two ways, directly and using

Stokes' Theorem.

NOTE: Enter the exact answers, $or$ round $to$ three decimal places.

Calculated directly: ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=$

Using Stokes' Theorem: ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r)=$