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arc_length_slides

# arc_length_slides - 2 a b dx Length of a curve x=g(y for c...

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Length of a smooth curve Summary of Sections 9.1 and 11.2

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3 ways to represent a smooth curve Graph of a differentiable function y=f(x) for a x b Graph of a differentiable function x=g(y) for c y d Parametric Equations : x=x(t) for t 1 t t 2 y=y(t) (for some differentiable functions x(t) and y(t))
Length of a curve y=f(x) for a x b L = 1 + ( f '( x )) 2 a b ! dx = 1 + dy dx " # \$ % & 2

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Unformatted text preview: 2 a b ! dx Length of a curve x=g(y) for c ≤ y ≤ d L = 1 + ( g '( y )) 2 c d ! dy = 1 + dx dy " # \$ % & ’ 2 c d ! dy d c x = g(y) Length of a curve given in parametric equations: x=x(t), y=y(t) for t 1 ≤ t ≤ t 2 L = dx dt ! " # \$ % & 2 + dy dt ! " # \$ % & 2 t 1 t 2 ’ dt t 2 =1 t 1 =-1 (x(t),y(t))...
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arc_length_slides - 2 a b dx Length of a curve x=g(y for c...

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