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Fundamental theorem of calculus for conservative fields

The fundamental theorem of calculus for conservative fieldsIf $f$ is differentiable and $\nabla f$ is continuous on a smooth curve $C$ given by the vector function MATH, $a\leq t\leq b$, thenMATH

Notice that the value of the integral depends only on the initial point MATH and the terminal point MATH, not on the particular way path that $C$ takes from MATH to MATH.


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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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