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Unformatted text preview: , f ( x i 1 )) and P i = ( x i , f ( x i )) = ( x i , y i ). We will define the length of the curve of y = f ( x ) over [ a , b ] , as Where the expression approximates the length of the curve of y = f ( x ) with a level of accuracy depending on the size of the number n . For each i, the MVT states that there exists an x i * in [ x i 1 , x i ] such that Then The last expression is a Riemann sum generated by the function [1 + f ( x ) 2 ] 1/2 . And so its limit as n tends to infinity is the definite integral of this function over [ a , b ]. So have So a formula for computing the curve length is 29.2 Example Compute the length of the arc of the parabola y = x 3/2 from (0, 0) to (1, 1). 29.3 Example Set up the integral (but do not solve) which can be used to compute the length of the portion of the curve of xy = 1 from the point (1, 1) to the point (2, )....
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- Spring '11