Applications of Integrals · Arc Length & Surface Area
Surface Area of Revolution
The surface area generated by revolving y = f(x) about the x-axis.
Conditions. f(x) ≥ 0 on [a, b].
- 2 variables
- 2 worked examples
- 14 in Applications of Integrals
Variables
| Symbol | Name | Unit |
|---|---|---|
| a | Left bound | - |
| b | Right bound | - |
Worked examples
Find the surface area when y = x on [0, 1] is revolved about the x-axis.
- f'(x) = 1. √(1+1) = √2
- S = 2π ∫₀¹ x · √2 dx = 2π√2 [x²/2]₀¹ = π√2
Answer: π√2 ≈ 4.443
1 more worked examplePremium
Find the surface area when y = 2x on [0, 1] is revolved about the x-axis.
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Practice
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