Parametric, Polar & Vectors · Parametric Curves
Parametric Arc Length
The length of a parametric curve from t = α to t = β.
- 2 variables
- 2 worked examples
- 12 in Parametric, Polar & Vectors
Variables
| Symbol | Name | Unit |
|---|---|---|
| alpha | Start parameter | - |
| beta | End parameter | - |
Worked examples
Find the circumference of x = cos t, y = sin t, 0 ≤ t ≤ 2π.
- dx/dt = -sin t, dy/dt = cos t
- √(sin²t + cos²t) = 1
- L = ∫₀^(2π) 1 dt = 2π
Answer: 2π
1 more worked examplePremium
Find the length of x = t², y = (2/3)t³ for 0 ≤ t ≤ 2.
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Practice
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