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Arc Length for Parametric Equations L = ∫ β α √( dx dt)2 +( dy dt)2 dt L = ∫ α β ( d x d t) 2 + ( d y d t) 2 d t Notice that we could have used the second formula for ds d s above if we

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Instead of having two formulas for the arc length of a function we are going to reduce it, in part, to a single formula. From this point on we are going to use the following