Chapter 18 Section 18.4 Another Notation for Line Integrals

Path Independence An integral is said to be path independent (or independent of path) if any two paths with the same initial and terminal points have the value of the integral over those paths equal. Conservative Vector Fields A vector field is conservative if energy is conserved along any path in the vector field. That is the energy expended moving to any position along any path is equal to the energy required to return to the same position along any other path possibly different path. The function that has the vector field as its gradient represents the potential energy and is called the potential function.

All of these have analogues statements for 3 dimensions.

x y