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.
- Spring '10