Let $Dbe$ the region between the circles $C_1$ and $C_2$ centered $at$ the origin $of$ radius $1$ and $4,$ respectively. Assume $C_1$ and $C_2$ are

oriented positively with respect $toD.$ Use the extended version $of$ Green's theorem for circulation $to$ calculate

$o{\displaystyle \underset{C_1}{\overset{\phantom{}}{}}}\frac{-2x}{\sqrt[\phantom{2}]{x^2+y^2}}dx+\frac{5y}{\sqrt[\phantom{2}]{x^2+y^2}}dy+o{\displaystyle \underset{C_2}{\overset{\phantom{}}{}}}\frac{-2x}{\sqrt[\phantom{2}]{x^2+y^2}}dx+\frac{5y}{\sqrt[\phantom{2}]{x^2+y^2}}dy.$