Calculating Work and Determining Conservativity for a Force F=(xy)i+(2*y^2)j

[brianeyes88677]

Homework Statement

A force F=(xy)i+(2*y^2)j，an object (mass=m) is move from (0,0) to (1,3) along y=3x , how much work does F do? Is F a conservative force?

Homework Equations

3. The Attempt at a Solution [/B]
Can I do it on the two axes?I mean ∫Fdx+∫Fdy , and because the work differ from the different road I take , F isn't a conservative force.
∫x*ydx=∫x*(3x)dx=1/3
∫2*y^2dy=36

 

[abbas_majidi]

If F be a conservative force yo can get work ∫Fdx+∫Fdy

 

[brianeyes88677]

Do I have to do ∫F⋅dr , where r=(1,3)/√10 ?

 

[abbas_majidi]

You can calculate curl of F if it will be zero F is conservative otherwise it isn't.

Path is clear and work is ∫F.dr, dr=dTI+3dtj and 0<t<1 whatever F be a conservative force or not.

 

[abbas_majidi]

Correction: 'dr=dti+3dtj'

 

[abbas_majidi]

I forgot tell you which x=t and y= 3t in above integral.