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Another Application: Arc Length (3/3/06) What is the length of a given arc? More specifically, given the function f (x), how long is the curve of f as x goes from a to b? Call this length s. Well, look at little short lengths s. By the Pythagorean Theorem, s (( x) 2 + ( y) 2 ) Factoring out x and going to the limit we get

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An Example of Arc Length Find the arc length of f (x) = x 2 as x runs from 0 to 2. The answer must be more than the straight line distance from (0,0) to (2,4), which is 2 5, or about 4.472. Well, which, sadly, is a tough one! So, use numerical integration: Simpson with n=2 gives (1 + 4( 2) + 2( 5) + 4( 10) + 17) / 6 4.650

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Assignment and look ahead We will have a regular class on Monday. The assignment for Monday is to read Section 8.1 and do Exercises 1, 3, 7, 11, 15, 17, 21 & 27. We will start Wednesday’s class in the regular classroom, then “adjourn” to the lab for Lab #4. On Friday we will have a 55 minute class, ending at 1:15 pm.

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