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

Section 1 Goals

• Apply the Fundamental Theorem of Calculus for lines integrals to evaluate a line integral of a conservative vector field.
• Articulate what it means for a region to be simply connected and recognize simply connected regions.
• Apply the curl test to determine whether a vector field is conservative.
• Articulate what it means for a vector field to be path-independent.
• Understand that a vector field is conservative on a given region if and only if it is path-independent on that region.
• Recognize a path-dependent vector field from its graph, and understand that this means the vector field is not conservative.