Calculus & Numerical Methods
Arc Length (numerical)
Length of curve y = f(x) on [a, b].
Formula
Formula
L = ∫ab√1 + f'(x)2 dx
Variables
| Symbol | Definition | Type & range | Units | Role |
|---|---|---|---|---|
| f | function | expression / text | x | input |
| a, b | limits | real number (ℝ) | — | input |
Try it yourself
Interactive calculator
Worked examples
Example 1
Givenf(x) = x*x, a = 0, b = 1, intervals n = 1000
Result1.478943007
Example 2
Givenf(x) = x, a = 0, b = 3, intervals n = 1000
Result4.242640687