16-2a - Math 200, Spring 2010 Handout #23 Section 16-2a...

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Math 200, Spring 2010 Handout #23 Section 16-2a Scalar Line Integrals Scalar Line Integral The line integral of a function ( ) , f x y over a curve C is called a scalar line integral and is denoted ( ) , C f x y ds . Conceptually, the scalar line integral is a limit of Riemann sums: Divide curve C into subarcs 1 i i P P with lengths i s Δ , choose a point ( ) * * * , i i i P x y on the i th subarc and form the Reimann sums ( ) * * 1 , i n i i i f x y s = Δ for a function f of two variables whose domain includes the curve C . The line integral of f along C is the limit (if it exists) of these Riemann sums as the maximum of the lengths i s Δ approaches zero: ( ) { } ( ) 0 * * 1 , lim , C i i n i i s i f x y ds f x y s Δ = = Δ If ( ) , 0 f x y , then ( ) , C f x y ds represents the area of one side of the “fence” whose base is C and whose height above the point ( ) , x y is ( ) , f x y . Computing a Scalar Line Integral Let C be a smooth curve given by parametric equations ( ) ( ) , , x x t y
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This note was uploaded on 02/24/2011 for the course MATH 200 taught by Professor Jamesdcampbell during the Spring '10 term at Santa Barbara City.

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16-2a - Math 200, Spring 2010 Handout #23 Section 16-2a...

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