Work done by force on moving particle

[PinkDaisy]

My problem is:

A particle is acted on by a force, F=-(5yx^2)i + (4y^3)j
Calculate the work done by F as the particle moves from point (-2,4) to point (5,10)? F is in Newtons and all x's and y's are in meters.

I think that I need to integrate each piece using the points as limits, but I'm not sure what I do with -(5yx^2) Do I only need to integrate with respect to x since it is with the "i" portion of the F?
Thanks!

 

[BLaH!]

The integral you evaluate when calculating work is called a "Path Integral". From the definition of work,

$$W = \int_a^b \vec F \cdot d\vec r = \int_a^b F_x dx + F_y dy + F_z dz$$

Thus you have three integrals: one over each coordinate.

So you are right...the integral over $$F_x$$ only affects the x variable.

 

[PinkDaisy]

Thanks so much!