< y^2, 2xy+ e^(3z), 3ye^(3z)> is the vector field.(adsbygoogle = window.adsbygoogle || []).push({});

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?...

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# An inconsistent conservative vector field

Loading...

Similar Threads - inconsistent conservative vector | Date |
---|---|

I Do time-dependent and conservative vector fields exist? | Oct 27, 2016 |

I Inconsistencies in the concept of limits | Jul 28, 2016 |

Integral inconsistency with variable change | Jun 22, 2015 |

3D Vector Inconsistency | May 21, 2011 |

Surface area of a cone-inconsistency? | Nov 12, 2009 |

**Physics Forums - The Fusion of Science and Community**