# Arc length and surface area

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Set up and simplify the integral that gives the length of the given smooth arc. Do not evaluate the integral.

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##### Solution Summary

This provides examples of setting up integrals to find arc length, and finding area of a surface of revolution.

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Set up and simplify the integral that gives the length of the given smooth arc. Do not evaluate the integral.

dy/dx = 5/2 x3/2

(dy/dx)2 = (5/2 x3/2)2 = 25/4 x3

ds = dx

ds = dx = dx

Arc length = dx

= dx

dy/dx = 4/3 x1/3

(dy/dx)2 = (4/3 x1/3)2 = 16/9 x2/3

ds = dx

ds = dx = dx = ...

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