University⏱ 4 min

Arc Length

Length of a curve via integral

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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.