# 11.17 - Section 13.2: Line integrals (concluded) In...

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Section 13.2: Line integrals (concluded) In analyzing C F d r = C ( F T ) ds , the sign of F T can be determined visually by looking at the angle θ between F and T . Since r ( t ) and T ( t ) are parallel and point in the same direction, the angle is is also the angle between F and r ( t ). Text question (page 936) Section 13.3: The fundamental theorem for line integrals Key ideas? ..?. . The fundamental theorem: C f d r = f ( r ( b )) – f ( r ( a )) The path-independence of C f d r (when C is smooth, f is differentiable, and f is continuous) Path independence the condition that C F d r = 0 for every closed curve C in the domain of F The equivalence of the following three conditions on a simply-connected domain: o Path independence o F = P i + Q j being conservative (i.e., F = f )

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o P / y = Q / x Conservation of energy The analogy beween the Fundamental Theorem of the Calculus and the fundamental theorem of line integrals:
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## This note was uploaded on 02/13/2012 for the course MATH 241 taught by Professor Staff during the Fall '11 term at UMass Lowell.

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11.17 - Section 13.2: Line integrals (concluded) In...

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