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Rizzi – Calc BC 7.4 Arc Length
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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
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Formula In terms of x In terms of y 𝑠= 𝑎 𝑏 1+ 𝑑𝑦 𝑑𝑥 2 𝑑𝑥
𝑠= 𝑎 𝑏 𝑑𝑦 𝑑𝑥 2 𝑑𝑥 In terms of x 𝑠= 𝑐 𝑑 𝑑𝑥 𝑑𝑦 2 𝑑𝑦 In terms of y
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Example 1 Find the arc length of the graph of 𝑦= 𝑥 𝑥 on the interval [ 1 2 , 2].
![Example 1 Find the arc length of the graph of 𝑦= 𝑥 𝑥 on the interval [ 1 2 , 2].](http://slideplayer.com./slide/15994345/88/images/4/Example+1+Find+the+arc+length+of+the+graph+of+%F0%9D%91%A6%3D+%F0%9D%91%A5+%F0%9D%91%A5+on+the+interval+%5B+1+2+%2C+2%5D..jpg "Example 1 Find the arc length of the graph of 𝑦= 𝑥 𝑥 on the interval [ 1 2 , 2].")
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Example 2 Find the arc length of the graph of 𝑦−1 3 = 𝑥 2 on the interval [0, 8].
![Example 2 Find the arc length of the graph of 𝑦−1 3 = 𝑥 2 on the interval [0, 8].](http://slideplayer.com./slide/15994345/88/images/5/Example+2+Find+the+arc+length+of+the+graph+of+%F0%9D%91%A6%E2%88%921+3+%3D+%F0%9D%91%A5+2+on+the+interval+%5B0%2C+8%5D..jpg "Example 2 Find the arc length of the graph of 𝑦−1 3 = 𝑥 2 on the interval [0, 8].")
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Homework P. 473 #3-15 odd
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