Calculus › Section O · Multiple integrals › Topic O.5
Surface area
How much fabric covers a curved roof? One double integral answers, and its integrand measures how the slopes stretch a flat patch onto the curve.
In this topic
- Measuring a curved skin
- Why the patch stretches: a cross product
- The surface area formula
- Worked example: a tilted plane
- Worked example: a paraboloid cap
- Worked example: a hemisphere, checked against history
- Strategy for setting up areas
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP