- #1
PFuser1232
- 479
- 20
The arc length of any curve defined by ##y = f(x)## is found as follows:
$$ds = \sqrt{dx^2 + dy^2}$$
$$ds = \sqrt{dx^2(1 + {\frac{dy}{dx}}^2)}$$
$$ds = \sqrt{dx^2} \sqrt{1 + [f'(x)]^2}$$
$$ds = \sqrt{1 + [f'(x)]^2} dx$$
Isn't ##\sqrt{dx^2}## equal to ##|dx|##, and not ##dx##?
$$ds = \sqrt{dx^2 + dy^2}$$
$$ds = \sqrt{dx^2(1 + {\frac{dy}{dx}}^2)}$$
$$ds = \sqrt{dx^2} \sqrt{1 + [f'(x)]^2}$$
$$ds = \sqrt{1 + [f'(x)]^2} dx$$
Isn't ##\sqrt{dx^2}## equal to ##|dx|##, and not ##dx##?