Math
Arc length.
Definition
The distance along a curved line. In calculus, the arc length of y = f(x) from x = a to x = b is found by integrating √(1 + [f′(x)]²) dx. In a circle, arc length equals the radius times the central angle in radians.
Examples
Real-world.
- 1 The arc length of a 60° (π/3 radian) arc on a circle of radius 6 is 6 · π/3 = 2π
- 2 Finding the length of y = x^(3/2) from x = 0 to x = 4 using the calculus formula
Key Fact
Circle: s = rθ; Calculus: L = ∫ from a to b √(1 + [f′(x)]²) dx