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A terrific, useful application of integrals is computing the arc length of a function. Here are formulas, examples, and notes.
Download Free Arc Length and Integrals.pdf file

Arc Length of a curve applications and examples from intmath.com
Video lesson of deriving arc length of curve and examples from profrobbob
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Math Cartoon #135 - Raiders of the Lost Arc (4-24-14)

Inside Math Archaeology
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