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
- dx/dt = -sin t, dy/dt = cos t
- √(sin²t + cos²t) = 1
- L = ∫₀^(2π) 1 dt = 2π
Answer: 2π
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Step-by-step solution locked.
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Common questions
What is the Parametric Arc Length?
The length of a parametric curve from t = α to t = β. It is one of the parametric, polar & vectors formulas in the CalcRef reference.
What do the symbols in the Parametric Arc Length mean?
In the Parametric Arc Length, alpha is the start parameter; beta is the end parameter.
How do you use the Parametric Arc Length?
Worked example. 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.
Practice
Quiz yourself on Parametric, Polar & Vectors
Parametric Arc Length is one of 12 Parametric, Polar & Vectors formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.