Calculus › Section H · Applications of integrals › Topic H.4
Arc length and surfaces of revolution
How long is a curved road, and how much material coats a curved pipe? Both answers come from the same picture: chop the curve into tiny straight pieces and let an integral add them up.
In this topic
- Measuring a curve with straight pieces
- The arc length formula
- Worked example: a curve with a neat length
- The straight-line check
- Arc length in the y-direction
- Surfaces of revolution: bands
- Worked example: the sphere formula
- Worked example: a surface about the y-axis
- Common mistakes to avoid
- Key takeaways
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Standards: 8 (BC)