Parametric, Polar & Vectors · Polar Coordinates

Polar Area

A=12αβ[r(θ)]2dθA = \frac{1}{2}\int_\alpha^\beta [r(\theta)]^2 \, d\theta

The area enclosed by a polar curve r = f(θ) from θ = α to θ = β.

  • 2 variables
  • 2 worked examples
  • 12 in Parametric, Polar & Vectors

Variables

Variables used in the Polar Area formula
SymbolNameUnit
alphaStart anglerad
betaEnd anglerad

Worked examples

Find the area enclosed by r = 2 (circle of radius 2).
  1. A = (1/2)∫₀^(2π) 4 dθ = 2(2π) = 4π

Answer:

1 more worked examplePremium

Find the area of one petal of r = sin(2θ).

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Practice

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