Calculus
Advanced

Arc Length (Integral)

Length of a curve y = f(x) from a to b.

Formula

L=∫ab1+(f′(x))2 dxL = \int_a^b \sqrt{1 + (f'(x))^2}\,dx

Variables

fFunction
a, bLimits

Example

For y = x from x=0 to 1: L = ∫√(1+1) dx = √2 ≈ 1.414.

Did You Know?

Measuring the length of a curve requires integrating the Pythagorean theorem over infinitely many tiny steps.

integralarc length