Applications of Integrals · Arc Length & Surface Area
Arc Length
The length of a curve y = f(x) from x = a to x = 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 arc length of y = x^(3/2) from x = 0 to x = 4.
- f'(x) = (3/2)x^(1/2). [f']² = (9/4)x
- L = ∫₀⁴ √(1 + 9x/4) dx. Let u = 1+9x/4, du = 9/4 dx
- = (4/9)·(2/3)[u^(3/2)]₁¹⁰ = (8/27)(10√10 - 1)
Answer: (8/27)(10√10 - 1) ≈ 9.073
1 more worked examplePremium
Find the arc length of y = (2/3)x^(3/2) from x = 0 to x = 3.
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Practice
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