Calculus › Section O · Multiple integrals › Topic O.3
Double integrals in polar coordinates
Describe a region by distance and angle and circular boundaries become constants. One extra factor of r is the whole price of the switch, and it unlocks even the famous Gaussian integral.
In this topic
- Circular regions fight rectangular coordinates
- Converting the pieces
- Why dA picks up a factor of r
- Worked example: area of a disk
- Worked example: volume under a paraboloid cap
- Regions traced by rays: the cardioid
- The Gaussian integral
- Choosing limits without tears
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP