Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.2 Length of a Plane Curve, #23 · Calculus · Applications of integrals

Instead of … a curve can be given as

Instead of $y = f (x)$ a curve can be given as $x = g (y)$ . Then
$d s = (d x)^{2} + (d y)^{2} = (d x / d y)^{2} + 1 d y .$
Draw $x = 5 y$ from $y = 0$ to $y = 1$ and find its length.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.2 Length of a Plane Curve, #23

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