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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, ½ )....
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This note was uploaded on 12/28/2011 for the course MATH 116 taught by Professor Robertandre during the Spring '11 term at Waterloo.
- Spring '11