Calculus

Arc Length

Length of a curve via integral

  • University
  • about 4 min
  • 19 of 31 in the family
Not started
Approx: 4.0909 (6 segments)
Segments: 6
b = 3.5
L=∫03.51+(f′)2 dx≈4.1303L = \int_0^{3.5}\sqrt{1+(f')^2}\,dx \approx 4.1303

Arc length = limit of sum of small straight line segments. The formula comes from the Pythagorean theorem applied to each infinitesimal piece.