Length of curves

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After completing this section, students should be able to do the following.

Apply the procedure of “Slice, Approximate, Integrate” to derive a formula for the length of a curve segment.
Understand the connection between the Pythagorean Theorem and the length of curves.
Set up an integral or sum of integrals with respect to $x$ and $y$ that gives the length of a curve segment.
Evaluate integrals that involve square roots.