Asked by Rob
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
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
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