m23 Arc Length

m23 Arc Length - MATH023 Arc Length Objectives At the end...

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MATH023 Arc Length
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Objectives At the end of the period, you should be able to: Determine the length of arc by integration. Derive common formulas of circumference and perimeter of geometric figures.
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Length Of Arc We want to determine the length of the continuous function y =f (x) on the interval [ a , b ]. a b
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Length Of Arc Initially we’ll need to estimate the length of the curve.
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Length Of Arc We’ll do this by dividing the interval into n equal subintervals each of width ∆x and we’ll denote the point on the curve at each point by P i . We can then approximate the curve by a series of straight lines connecting the points.
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Length Of Arc Consider the graph. Now denote the length of each of these line segments by and the length of the curve will then be approximately
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Length Of Arc We can get the exact length by taking n larger and larger. In other words, the exact length will be,
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Length Of Arc We can then compute directly the length of the line segments as follows. By the Mean Value Theorem we know that on the interval, Therefore, the length can now be written as,
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Length Of Arc The exact length of the curve is then, Using the definition of the definite integral , this is nothing more than, or
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When the equation of the curve is given in non- parametric form y = f(x) , a x b. dx
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This note was uploaded on 12/08/2011 for the course ECON 101 taught by Professor Smith during the Spring '11 term at Adrian College.

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m23 Arc Length - MATH023 Arc Length Objectives At the end...

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