Calculus › Section K · Conics, parametric equations, and polar coordinates › Topic K.5
Area and arc length in polar coordinates
In polar coordinates the natural building block is not a rectangle but a thin slice of pie. That one change makes areas of petals, cardioids and spirals into short integrals, and it hands arc length a strikingly simple formula.
In this topic
- Sectors, not rectangles
- The polar area formula
- Worked example: area inside a cardioid
- Area between two polar curves
- Worked example: between two circles
- Arc length in polar form
- Worked example: perimeter of a cardioid
- Surfaces of revolution in polar form
- Common mistakes to avoid
- Key takeaways
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Standards: 9 (BC)