Let $F=$grad$(x^3{y}^2)$ and let $Cbe$ the path $in$ the $xy-$plane from $(-8,8)to(8,8)$ that

consists $of$ the line segment from $(-8,8)to(0,0)$ followed $by$ the line segment

from $(0,0)to(8,8).$ Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*drin$ two ways.

$aC$ and evaluate the integral.

$bf(x,y)=x^3{y}^{2}as$ a potential function for $F.$

$a\{$:$C_1$:$r_1(t)=1,)i+(8-8t)j,0t1$

$C_2$:$r_2(t)=(8t)i+(,)j,0t1$