Unformatted text preview: curve. As usual, we need to think about how we might approximate the length, and turn the approximation into an integral. We already know how to compute one simple arc length, that of a line segment. If the endpoints are P ( x , y ) and P 1 ( x 1 , y 1 ) then the length of the segment is the distance between the points, p ( x 1x ) 2 + ( y 1y ) 2 , from the Pythagorean theorem, as illustrated in ﬁgure 9.19 . ....................................................................................... ( x 1 , y 1 ) ( x , y ) x 1x y 1y p ( x 1x ) 2 + ( y 1y ) 2 Figure 9.19 The length of a line segment. Now if the graph of f is “nice” (say, diﬀerentiable) it appears that we can approximate the length of a portion of the curve with line segments, and that as the number of segments...
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 Spring '07
 JonathanRogawski
 Math, Calculus, Normal Distribution, Probability, Variance, Probability theory, probability density function

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