Posted by Rob on Tuesday, December 4, 2007 at 2:44am.
For a smal change in x, dx:
ds² = dx² + dy²
ds = sqrt [(dx² + dy²)]
s = INTEGRAL of sqrt [(dx² + dy²)]
s = INTEGRAL of sqrt [(dx² + dy² * dx²/dx²)]
s = INTEGRAL of sqrt[(1 + dy² * 1/dx²)] dx
s = INTEGRAL of sqrt[(1 + (dy/dx)²)] dx

Is this how you derive the formula for arc length?  drwls, Tuesday, December 4, 2007 at 8:13am
Yes; that is one way.

Is this how you derive the formula for arc length?  Matt, Tuesday, December 4, 2007 at 11:09am
in the third step, how did you integrate the right side with no deltavariable?

Is this how you derive the formula for arc length?  drwls, Tuesday, December 4, 2007 at 11:12am
There is a delta variable dx. You must compute and insert dy/dx into the integrand to get the resulting arc length
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