Finding the potential energy function( I don't know how the answer came to be)

[Raziel2701]

Homework Statement

The give force is conservative $$F=A(y,x,0)$$ where A is a constant.

The Attempt at a Solution

To find the potential function we integrate the negative of the force. Setting the potential U to be zero at the origin, we can integrate over an easy path, so I think going over to the x direction once, and then up in the y direction could work right?

So here are the two integrals(the z-direction force is zero so it's integral would be zero as well.

$$-A\int_0 ^x y' dx' +-A\int_0 ^y x' dy'$$

If I do those integrals I get -2Axy, yet the answer is supposed to be -Axy, I'm wondering if maybe the path I'm using is wrong?

 

[tiny-tim]

Hi Raziel2701!

The first integral (over x) has to be at y = 0, so it's zero.

(the second integral (over y) is at x = x)

(btw, isn't it obvious that (y,x,0) = grad(xy) ? )