Let $F=$grad$(x^5{y}^4)$ and let $C$ be the path in the $xy-$plane from $(-4,4)$ to $(4,4)$ that consists of the line segment from $(-4,4)$ to $(0,0)$ followed by the line segment from $(0,0)$ to

$(4,4).$ Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr$ in two ways.

a$)$ Find parametrizations for the segments that make up C and evaluate the integral.

b$)$ Use $f(x,y)=x^5{y}^4$ as a potential function for $F.$