Let $F=$grad$(x^7{y}^6)$ and let $Cbe$ the path $in$ the $xy-$plane from $(-2,2)to(2,2)$ that consists $of$ the line segment from

$(-2,2)to(0,0)$ followed $by$ the line segment from $(0,0)to(2,2).$ Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*drin$ two ways.

$aC$ and evaluate the integral.

$bf(x,y)=x^7{y}^{6}as$ a potential function for $F.$

$aC.$

$C_1$:$r_1(t)=(,)i+(2-2t)j,0t1$

$C_2$:$r_2(t)=(2t)i+(,)j,0t1$