Green's Theorem helps us understand where the conservative vector field test comes from (for a planar field).
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Video 16.8.4: More Notes on Stokes' Theorem
Video 16.5 Addendum: A Point-Wise Interpretation of Curl
Video 16.8.2: Using Stokes' Theorem to Evaluate a Line Integral
Video 16.8.1: Introduction to Stokes' Theorem
16.6.3B: Parameterizing the Lower Half of an Ellipsoid
Video 16.4.7: Green's Theorem Ties Up a Loose End
Video 16.4.6: Conservative Vector Fields, Path Independence, and Line Integrals on Closed Curves
Video 16.4.5: Using a Line Integral of Compute the Area of a Region
Video 16.4.4: Green's Theorem Extended to a Region with a Hole
Video 16.4.3: Green's Theorem on a Heart-Shaped Region
Video 16.4.2: Partial Proof of Green's Theorem
Video 16.4.1: Green's Theorem with a Quick Example
Video 16.1.1: Introduction to Vector Fields (Redux)
Video 16.3.4: Recovering a Potential Function from F(x,y)
Video 16.3.3: Showing a 2D Vector Field is Conservative
Video 16.3.2: Evaluating a Line Integral using the Fundamental Theorem of Line Integrals
Video 16.3.1: The Fundamental Theorem of Line Integrals
Video 16.2.8: The Sign of a Line Integral Over a Vector Field From Its Graph
Video 16.2.7: Evaluating a Line Integral in Differential Form
Video 16.2.5: Computing a Line Integral W.R.T. a Vector Field
Video 16.2.4: Line Integrals W.R.T. a Vector Field
Video 16.2.2: Arc Length Line Integrals Part 2
Video 16.2.1:Introduction to Line Integrals w.r.t. Arc Length
Video 16.2.3: Example of Arc Length Integration