Parametric, Polar & Vectors · Polar Coordinates
Polar Area
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
| Symbol | Name | Unit |
|---|---|---|
| alpha | Start angle | rad |
| beta | End angle | rad |
Worked examples
Find the area enclosed by r = 2 (circle of radius 2).
- A = (1/2)∫₀^(2π) 4 dθ = 2(2π) = 4π
Answer: 4π
1 more worked examplePremium
Find the area of one petal of r = sin(2θ).
Step-by-step solution locked.
Unlock the full working. CalcRef Premium opens the step-by-step solution above, and 141 worked solutions across the whole library - the intermediate lines, not just the answer. The formula statement, its conditions, its variables and the first worked example stay free on every page.
See all 12 Parametric, Polar & Vectors formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.
Practice
Quiz yourself on Parametric, Polar & Vectors
Polar 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.