Calculus › Section O · Multiple integrals › Topic O.2
Double integrals and volume
Rectangles were a warm-up. Real regions sit between curves, and their double integrals measure volumes of solids that no single-variable method can reach.
In this topic
- Adding columns over a region
- Regions between curves
- Worked example: volume between two parabolas
- Horizontally simple regions
- Worked example: a triangle, both ways
- Reversing the order to escape a trap
- Properties and a shortcut
- Signed volume and applications ahead
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP