RedAssign8[1].1 - Pick two points on the curve that are...

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Unit: Applications of Integral Calculus Module: Arc Length Introduction to Arc Length www.thinkwell.com [email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved. 1604 –rev 06/14/2001 Arc length is the length of the curve. The arc length of a smooth curve given by the function f ( x ) between a and b : + 2 1[() ] b a fx d x . When measuring how long a line is, you can just use a ruler or the distance formula. But curves are trickier. It would be good to have a way to measure their lengths. This length is called arc length . One way to think about arc length is to break a curve up into a lot of line segments. Then you can approximate the arc length by adding them all up. To find the exact arc length you have to use
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Unformatted text preview: Pick two points on the curve that are very close to each other. The second point is a small change in x from the first point. The Pythagorean theorem tells you the length of the line segment connecting the two points. Notice that the length of the line segment is expressed in terms of the change in the two directions. To find the length of the entire curve, you must sum up the lengths of all the line segments. Factoring out a ∆ x moves the small change in x outside the radical sign. If you let ∆ x become arbitrarily small, then it acts like a dx . Then you can find the arc length by integrating. Notice that the integral is different from the integral you would use to find the area under the curve....
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This note was uploaded on 04/27/2010 for the course MATH 172 taught by Professor Hyon during the Spring '10 term at Community College of Denver.

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