CALCULUS Understanding Its Concepts and Methods

Fundamental theorem of calculus for conservative fields

The fundamental theorem of calculus for conservative fieldsIf is differentiable and is continuous on a smooth curve given by the vector function , , then

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

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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.