Arc Length with Parametric Equations

# Arc Length with Parametric Equations - Arc Length with...

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Arc Length with Parametric Equations In the previous two sections we’ve looked at a couple of Calculus I topics in terms of parametric equations. We now need to look at a couple of Calculus II topics in terms of parametric equations. In this section we will look at the arc length of the parametric curve given by, We will also be assuming that the curve is traced out exactly once as t increases from α to β. We will also need to assume that the curve is traced out from left to right as t increases. This is equivalent to saying, So, let’s start out the derivation by recalling the arc length formula as we first derived it in the arc length section of the Applications of Integrals chapter. where,

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We will use the first ds above because we have a nice formula for the derivative in terms of the parametric equations (see the Tangents with Parametric Equations section). To use this we’ll also need to know that, The arc length formula then becomes,
This is a particularly unpleasant formula. However, if we factor out the denominator

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## This note was uploaded on 11/10/2011 for the course MATH 136 taught by Professor Prellis during the Fall '08 term at Rutgers.

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Arc Length with Parametric Equations - Arc Length with...

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