Find work given force equation in component form

[xcgirl]

Homework Statement

First, there is a graph showing x initial at (0,0) and x final at (1,1)

Given: F = xy i +xyj
Find the work done by this force moving the particle from x initial to x final. [note you'll need a relationship between y and x]

Homework Equations

W = Fdcos(theta)
Work is the integral of force

The Attempt at a Solution

I know that the relationship between y and x is simply y = x. So would i just subsitute y for x in the force equation and integrate from 0 to 1? What trips me up is that the force equation is given in component form, and I'm not sure how to integrate with it in that way.

Thank you for any help in advance

 

[Redbelly98]

The Attempt at a Solution

I know that the relationship between y and x is simply y = x. So would i just subsitute y for x in the force equation and integrate from 0 to 1?

Yes.

What trips me up is that the force equation is given in component form, and I'm not sure how to integrate with it in that way.

Since they give you the components of F, you can use that information to figure out the angle between F and the direction of the displacement. You pretty much need to know this angle, since (as you correctly said) W = F·d·cosθ