Chap13sec3

Chap13sec3 - Now in section 13.3 we see yet another way to determine arc length by using a vector function Suppose that the helix 3cos,3sin,0.25 t

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13.3 Arc Length and Curvature There are several approaches to finding the length of a portion of the graph of a function.  In section 8.1 arc length is found using integrals and derivatives. From 8.1 (page 542), If  ' f  is continuous on [a,b], then the length of the curve  ( 29 , , y f x a x b =  is ( 29 2 1 ' b a L f x dx = + In section 10.3, a formula for arc length is given for the parametric equations  ( ), ( ), x f t y g t t α β = = ≤ ≤ , but  there are some restrictions (see page 656). 2 2 dx dy L dt dt dt = + Arc length can also be found for a polar curve,  2 2 b a dr L r d d θ = +   (see page 673 for the restrictions and details.)
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Unformatted text preview: Now in section 13.3 we see yet another way to determine arc length by using a vector function. Suppose that the helix ( ) 3cos( ),3sin( ),0.25 t t t t = r shown below (and seen in the notes of section 13.1) is a piece of string. If we straighten out the string and measure its length we get its arc length. To compute the arc length, we use the formula [ ] [ ] [ ] 2 2 2 '( ) '( ) '( ) '( ) b b a a L t dt f t g t h t dt = = + + ∫ ∫ r Example: Find the arc length of the helix shown over [0,7 π ]....
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This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.

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