The arc length of any curve defined by ##y = f(x)## is found as follows:(adsbygoogle = window.adsbygoogle || []).push({});

$$ds = \sqrt{dx^2 + dy^2}$$

$$ds = \sqrt{dx^2(1 + {\frac{dy}{dx}}^2)}$$

$$ds = \sqrt{dx^2} \sqrt{1 + [f'(x)]^2}$$

$$ds = \sqrt{1 + [f'(x)]^2} dx$$

Isn't ##\sqrt{dx^2}## equal to ##|dx|##, and not ##dx##?

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# Arc length

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