Let vec$(F)=(6x^{2}y+2y^3+2e^x)vec(i)+(4e^{y^2}+96x)vec(j).$ Consider the line

integral $of$ vec$(F)$ around the circle $of$ radius $a,$ centered $at$ the origin and

traversed counterclockwise.

$(a)$ Find the line integral for $a=1.$

line integral $=$

$(b)$ For which value $ofais$ the line integral a maximum?

$a=$

$(Be$ sure you can explain why your answer gives the correct maximum.$)$