Finding Work Done by a Force on a Particle Along a Triangular Path

[S[e^x]=f(u)^n]

Homework Statement

F=(5y+3x-6)i + (2x-y+4)j. find work done by the force on a particle following a triangular path with verticies (0,0),(4,0),(4,3) where the positions are given in meters.

Homework Equations

Int(F(x,y))dx*dy ? not really sure for 2 dimensional problems

The Attempt at a Solution

I integrated the force equation with respect to x and then y to obtain...
2xy(5y+3x-3)i + xy(x-(1/2)y+4)j and then calculated the work for each section of the path and added them together. i don't think its the right way to do it though. Is there a way to solve this without the need for line integrals!? Please help

 

[S[e^x]=f(u)^n]

bump. basically i need to know how to figure out work done over a non uniform 2 dimensional field. even if it requires line integrals, if someone could walk me through it

 

[S[e^x]=f(u)^n]

nobody knows? did i phrase my question wrong or something?