$($a$)$ Find a parameterization $$r $1($t$)$ of half of the circle radius $1,$ centered at $(1,0),$ going from $(2,0)$ to $(0,0)$ in

a counterclockwise fashion. Hint: for general ellipses in standard orientation, a valid parameterization

looks like $$x$0+$ a cos$($t$),$ y$0+$ b sin$($t$).$

$($b$)$ For the vector field $$ F $($y$)=$y$,1$ y$2,$ calculate R

C $$ F $$ d $$r $1.$

$($c$)$ Find a parameterization $$r $2($t$)$ of a line segment going from $(0,0)$ to $(2,0).$

$($d$)$ Once again calculate R

C $$ F $$ d $$r $2.$

$($e$)$ Make a small sketch of the oriented path which combines parts $($a$)$ and $($c$).$ Apply Green$$s Theorem

and compare the result with the sum of the line integrals.