Let $F=($:$x,y$:$)$ and $C$ be the triangle with vertices $(0,+-2)$ and $(3,0)$ oriented counterclockwise. Evaluate $o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr$ by parameterizing $C.$

Use a parametric description of C and set up the integral.

$o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr={\displaystyle \underset{0}{\overset{1}{}}},dt$

Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.

A$.$ For $F=$grad$$ and $r(t)=($:$x(t),y(t)$:$),$ evaluating the integral using $\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{x}}=,$ and $\frac{\text{d}\text{e}\text{l}}{\text{d}\text{e}\text{l}\text{y}}=$ results in a nonzero value of $$

B$.$ For $F=($:$f,g$:$)$ and $r(t)=($:$x(t),y(t)$:$),$ evaluating the integral using $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}=$ and $\frac{\text{d}\text{e}\text{l}\text{g}}{\text{d}\text{e}\text{l}\text{x}}=$ results in a nonzero value of $$

c$.$ For $F=(f,g)$ and $r(t)=($:$x(t),y(t)),$ evaluating the integral using $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}=$ and $\frac{\text{d}\text{e}\text{l}\text{g}}{\text{d}\text{e}\text{l}\text{y}}=$ results in a nonzero value of