- #1

riemannsigma

- 10

- 0

the above vector field is inside an open simply connected domain.

the parametric equations all have a continuous first order derivative inside the domain.

Lastly, the curl of the vector field is <0, 0, 0>

Thus, the vector field is conservative and is path independent.

HOWEVER...

If i take the

x axis, y axis, and z axis,

Y axis, x axis, and z axis, OR

Y axis, z axis, and x-axis

pathways, then I get the scalar field equation to be

[f(x,y,z)] = xy^2 + y + ye^(3z)

This is NOT CORRECT!

If I take the three axis pathways in any other order than the order listed above, then I get the correct answer.

Correct function is

[f(x,y,z)] = xy^2 + ye^(3z)There is not doubt that the vector field is conservative.

If a vector field is conservative, then the path integral MUST BE path independent.

Why do I get two different answers?...