Consider the following vector field $F(x,y)=MiNj.$

$F(x,y)=yixj$

$($a$)$ Show that $F$ is conservative.

$\frac{\text{d}\text{e}\text{l}\text{N}}{\text{d}\text{e}\text{l}\text{x}}=\frac{\text{d}\text{e}\text{l}\text{M}}{\text{d}\text{e}\text{l}\text{y}}=$

$$

$($b$)$ Verify that the value of ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr$ is the same for each parametric representation of $C.$

$($i$)$

$C_1$:$r_1(t)=(8t)i(9-t)j,0t1$

${\displaystyle \underset{C_1}{\overset{\phantom{}}{}}}F*dr=$

$($ii$)$

$C_2$:$r_2(w)=(8ln(w))i(9-ln(w))j,1we$

${\displaystyle \underset{C_2}{\overset{\phantom{}}{}}}F*dr=$