Find the flow of the velocity field $F=(9y^2+1)i+(18xy)j$ along each of the following paths from $(0,0)$ to $(2,1).$

a$.$

b$.$

c$.$ Use any path from $(0,0)$ to $(2,1)$ different from parts $($a$)$ and $($b$).$

a$.$ The flow of the velocity field is