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# notes19 - f ( x ) = x 3 / 2 Math 9C Fall 2011 (UCR)...

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Arc Length In class we leaned that to compute the length s of a curve given as the graph of some function f ( x ) between x = a and x = b we compute ds = q 1 + ( f 0 ( x )) 2 dx . To ﬁnd s when then compute s = Z b a ds = Z b a q 1 + ( f 0 ( x )) 2 dx Math 9C Fall 2011 (UCR) Pro-Notes November 13, 2011 1 / 4

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Example Compute the length of the curve given by the equation y 2 = x 3 between the points (1 , 1) and (4 , 8). We ﬁrst rewrite y 2 = x 3 so that the curve can be expressed as the graph of some function f ( x ). By solving for y we obtain y = ± x 3 / 2 . Since we are only concerned about the potion of this curve between the points (1 , 1) and (4 , 8), we need to only consider the positive par, that is we can let

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Unformatted text preview: f ( x ) = x 3 / 2 Math 9C Fall 2011 (UCR) Pro-Notes November 13, 2011 2 / 4 Now f ( x ) = (3 / 2) x 1 / 2 so ds = q 1 + ((3 / 2) x 1 / 2 ) 2 dx = p 1 + 9 / 4 xdx . Making the substitution u = 1 + 9 / 4 x we compute the length s as s = Z 4 1 p 1 + 9 / 4 xdx = 4 / 9 Z 10 13 / 4 udu Math 9C Fall 2011 (UCR) Pro-Notes November 13, 2011 3 / 4 = 4 / 9 2 / 3 u 3 / 2 | 10 13 / 4 = 8 / 27(10) 3 / 2-8 / 27(13 / 4) 3 / 2 . Math 9C Fall 2011 (UCR) Pro-Notes November 13, 2011 4 / 4...
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## This note was uploaded on 02/22/2012 for the course MATH 9c taught by Professor C during the Fall '11 term at UC Riverside.

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notes19 - f ( x ) = x 3 / 2 Math 9C Fall 2011 (UCR)...

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