Quick question regarding work?

1. The problem statement, all variables and given/known data
A force in the xy plane is given by F = A(10ai + 3xj), where A and a are constants, F is in newtons and x is in meters. Suppose that the force acts on a particle as it moves from an initial position x = 4m, y = 1m to a final position x = 4m, y = 4m. Show that this force is not conservative by computing the work done by the force for at least two different paths.


2. Relevant equations
W = integral of f dx


3. The attempt at a solution
I basically integrated and got W = A(10axi + 3/2 x^2j)
I'm not sure how to exactly calculate the work done across the paths though.

thanks.

 

yeah I forgot how to compute the work from one point to another point.

 

yeah I know you have to integrate the force vector across the displacement since it varies with displacement. I don't know how exactly you do that across the points. Do you have to do line integrals or something?

 

thanks. how exactly do you compute the line integral again?
We didn't get up to it yet, we're only doing double integrals in multi.

 

any ideas