Path independence for line integrals | Multivariable Calculus | Khan Academy

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Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/multivariable-calculus/integrating-multivariable-functions/line-integrals-vectors/v/path-independence-for-line-integrals Showing that if a vector field is the gradient of a scalar field, then its line integral is path independent Watch the next lesson: https://www.khanacademy.org/math/multivariable-calculus/line_integrals_topic/line_integrals_vectors/v/closed-curve-line-integrals-of-conservative-vector-fields?utm_source=YT&utm_medium=Desc&utm_campaign=MultivariableCalculus Missed the previous lesson? https://www.khanacademy.org/math/multivariable-calculus/line_integrals_topic/line_integrals_vectors/v/vector-field-line-integrals-dependent-on-path-direction?utm_source=YT&utm_medium=Desc&utm_campaign=MultivariableCalculus Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to

Published 2010-03-05 · Watch on YouTube ↗
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