Let $\vec F = (6 x^2 y + 2 y^3 + 3 e^x)\,\vec i + (7 e^{y^2} + 54 x)\,\vec j$. 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.)