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Conservative Fields & Path Independence (Vector Fields)

Calculus 3 tutorial video that explains path independence and conservative vector fields, as well as the Fundamental Theorem of Line Integrals. We show you shortcuts that are available when calculating line integrals of vector fields, if that field is conservative (path independent). We discuss how the work around a closed curve is zero in a conservative field, and give a general outline for the most efficient way to calculate line integrals. A few examples are worked to demonstrate these new line integral shortcuts! 0:00 Gradient/Conservative/Path Independent 2:10 Fundamental Theorem of Line Integrals 3:06 Example 6:05 Closed Curves in Gradient Fields 7:23 Examples 10:37 Outline for Line Integral Efficiency Houston Math Prep Calculus 3 Playlist:    • Calculus 3   Houston Math Prep YouTube:    / houstonmathprep