Suppose vec$(F)=(5x-2y)vec(i)+(x+5y)vec(j).$ Use Stokes' Theorem to make the following circulation calculations.

$($a$)$ Find the circulation of vec$(F)$ around the circle $C$ of radius $8$ centered at the origin in the xy$-$plane, oriented clockwise as viewed from the positive z $-$axis.

PROGRESS

Circulation $={\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(s)=$

$q,$

$($b$)$ Find the circulation of vec$(F)$ around the circle $C$ of radius $8$ centered at the origin in the yz$-$plane, oriented clockwise as viewed from the positive x $-$axis.

Circulation $={\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(s)=$

$$