Applications of Integrals · Volume
Disk Method
Volume of revolution about the x-axis when there is no gap between the curve and the axis. Each cross-section is a disk with radius f(x).
- 2 variables
- 2 worked examples
- 14 in Applications of Integrals
Variables
| Symbol | Name | Unit |
|---|---|---|
| a | Left bound | - |
| b | Right bound | - |
Worked examples
- V = π ∫₀⁴ (√x)² dx = π ∫₀⁴ x dx = π[x²/2]₀⁴ = π(8) = 8π
Answer: 8π ≈ 25.13
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Common questions
What is the Disk Method?
Volume of revolution about the x-axis when there is no gap between the curve and the axis. Each cross-section is a disk with radius f(x). It is one of the applications of integrals formulas in the CalcRef reference.
What do the symbols in the Disk Method mean?
In the Disk Method, a is the left bound; b is the right bound.
How do you use the Disk Method?
Worked example. Find the volume when y = √x is revolved about the x-axis on [0, 4]. V = π ∫₀⁴ (√x)² dx = π ∫₀⁴ x dx = π[x²/2]₀⁴ = π(8) = 8π. Answer: 8π ≈ 25.13.
Practice
Quiz yourself on Applications of Integrals
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