$Ex3.$ Let $(x,y)=\frac{x^2-y^2}{2}$ and $F=$grad$=($:$x,-y$:$).$ Evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F*dr$ for

$(a)C$ the quarter circle from $(1,0)to(0,1)$

$(b)C$ the line