Determine if vec$(F)=$ is conservative. If it is$,$ find a potential function f such that gradf$=$vec$(F).$ Then, use the potential function to evaluate the following integral:

${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)dvec(r)$

where C is the semicircle from $(0,1)$ to $(2,1).$

Is $F$ conservative? $($Type yes or no$).$ You must show work on paper for credit.

A$)$

Give a potential function:

$$

Value of ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*vec(dr)$

$$ A