Parametric, Polar & Vectors · Parametric Curves
Parametric Area
The area under a parametric curve. More precisely, the signed area between the curve and the x-axis.
- 2 worked examples
- 12 in Parametric, Polar & Vectors
Worked examples
- A = -∫₀^(2π) sin t · (-sin t) dt = ∫₀^(2π) sin²t dt
- = ∫₀^(2π) (1-cos2t)/2 dt = [t/2 - sin2t/4]₀^(2π) = π
Answer: π
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Common questions
What is the Parametric Area?
The area under a parametric curve. More precisely, the signed area between the curve and the x-axis. It is one of the parametric, polar & vectors formulas in the CalcRef reference.
How do you use the Parametric Area?
Worked example. Find the area enclosed by x = cos t, y = sin t (circle of radius 1). A = -∫₀^(2π) sin t · (-sin t) dt = ∫₀^(2π) sin²t dt. = ∫₀^(2π) (1-cos2t)/2 dt = [t/2 - sin2t/4]₀^(2π) = π. Answer: π.
Practice
Quiz yourself on Parametric, Polar & Vectors
Parametric Area 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.