Let vec$(F)=(9x^{2}y+3y^3+5e^x)vec(i)+(5e^{y^2}+81x)vec(j).$ 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 of $a$ is the line integral a maximum?

$a=$

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