Rizzi – Calc BC 7.4 Arc Length.

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Presentation transcript:

Rizzi – Calc BC 7.4 Arc Length

Purpose: Find Length of a Curve Terminology: Rectifiable: a curve that has a finite arc length To find arc length, you need a curve that is continuous and differentiable MUST BE A FUNCTION

Formula In terms of x In terms of y 𝑠= 𝑎 𝑏 1+ 𝑑𝑦 𝑑𝑥 2 𝑑𝑥 𝑠= 𝑎 𝑏 1+ 𝑑𝑦 𝑑𝑥 2 𝑑𝑥 In terms of x 𝑠= 𝑐 𝑑 1+ 𝑑𝑥 𝑑𝑦 2 𝑑𝑦 In terms of y

Example 1 Find the arc length of the graph of 𝑦= 𝑥 3 6 + 1 2𝑥 on the interval [ 1 2 , 2].

Example 2 Find the arc length of the graph of 𝑦−1 3 = 𝑥 2 on the interval [0, 8].

Homework P. 473 #3-15 odd