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.
- 0 variables
- 2 worked examples
- 12 in Parametric, Polar & Vectors
Worked examples
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
1 more worked examplePremium
Find the area under one arch of the cycloid x = t - sin t, y = 1 - cos t, 0 ≤ t ≤ 2π.
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Practice
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