Question

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

Answer 1

Yes; that is one way.

Answer 2

in the third step, how did you integrate the right side with no delta-variable?

Answer 3

There is a delta variable dx. You must compute and insert dy/dx into the integrand to get the resulting arc length