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# 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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https://brainmass.com/math/integrals/arc-length-surface-area-254331

#### Solution Preview

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 = ...

#### 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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