Applications of Integrals · Centroids & Averages
Centroid (x-coordinate)
The x-coordinate of the centroid of the region between f(x) and g(x). A is the area of the region.
- 2 variables
- 2 worked examples
- 14 in Applications of Integrals
Variables
| Symbol | Name | Unit |
|---|---|---|
| a | Left bound | - |
| b | Right bound | - |
Worked examples
Find x̄ for the region under y = x² on [0, 2].
- A = ∫₀² x² dx = 8/3
- x̄ = (3/8) ∫₀² x · x² dx = (3/8) ∫₀² x³ dx = (3/8)(4) = 3/2
Answer: x̄ = 3/2
1 more worked examplePremium
Find x̄ for the triangular region under y = x on [0, 3].
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Practice
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