Calculus · PAR
Area in Polar Coordinates — A = (1/2)∫r² dθ
Area enclosed by polar curve r = f(θ) from α to β: A = (1/2)∫[α,β] [f(θ)]² dθ.
CalculusCommon Core CHA-5.DPARVerified correct ✓
Worked examples
Find the area enclosed by the polar curve r = 3 (a full circle) using A = (1/2)∫[0,2π] r² dθ. Round to 4 decimal places.
Answer: 28.2743
Find the area enclosed by the polar curve r = 4 (a full circle) using A = (1/2)∫[0,2π] r² dθ. Round to 4 decimal places.
Answer: 50.2655
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