handout 13-3 - Math 200, Spring 2010 Handout 7 Section 13-3...

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Math 200, Spring 2010 Handout 7 Section 13-3 Arc Length and Speed Arc Length of a Plane Curve (Path) The length L of plane curve C defined by the parametric equations ( ) x x t = , ( ) y y t = , a t b ≤ ≤ , where functions x and y are continuous on , a b and C is traversed exactly once, is given by ( ) ( ) 2 2 b a L x t y t dt = + For plane path ( ) ( ), ( ) t x t y t = r , ( ) b a L t dt = r since ( ) ( ) ( ) ( ) ( ) 2 2 , t x t y t x t y t = = + r Arc Length of a Space Curve (Path) The length L of space curve C defined by the parametric equations ( ) ( ) ( ) , , x x t y y t z z t = = = , a t b ≤ ≤ , where functions , and x y z are continuous on , a b and C is traversed exactly once, is given by ( ) ( ) ( ) 2 2 2 b a L x x y x z x dt = + + For path ( ) ( ), ( ), ( ) t
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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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handout 13-3 - Math 200, Spring 2010 Handout 7 Section 13-3...

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