The Fundamental Theorem of Calculus for Line Integrals and Path-Independent Vector Fields

The Fundamental Theorem of Calculus for Line Integrals and Path-Independent Vector Fields

In single variable calculus, one of the main tools used to calculate a definite integral is the Fundamental Theorem of Calculus. A similar result holds for line integrals, though it can only be applied to conservative vector fields. This means the problem of deciding whether or not a given vector field is conservative is front and center when it comes to evaluating line integrals.

This worksheet states the Fundamental Theorem of Calculus for line integrals and explores how to apply it. It also introduces techniques for deciding whether or not a given vector field is conservative, and describes the relationship between path independence and conservative vector fields.