Posted by Rob on .
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,
Yes; that is one way.

Is this how you derive the formula for arc length? 
Matt,
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,
There is a delta variable dx. You must compute and insert dy/dx into the integrand to get the resulting arc length