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 delta-variable?

- 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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