Therefore, the arc length can be written as, L =∫ b a ∥∥→r ′(t)∥∥ dt L = ∫ a b ‖ r → ′ ( t) ‖ d t Let’s work a quick example of this. Example 1 Determine the length of the curve →r (t) =

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r'(t) = (0,1,2t) Arc length is given by: L = ∫ 1 0 √02 +12 + (2t)2dt. Simplify: L = ∫ 1 0 √1 + 4t2dt. Apply the substitution 2t = tanθ: L = 1 2∫sec3θdθ. This is a known integral. If you do not