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
- 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
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Common questions
What is the 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. It is one of the applications of integrals formulas in the CalcRef reference.
What do the symbols in the Centroid (x-coordinate) mean?
In the Centroid (x-coordinate), a is the left bound; b is the right bound.
How do you use the Centroid (x-coordinate)?
Worked example. 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.
Practice
Quiz yourself on Applications of Integrals
Centroid (x-coordinate) is one of 14 Applications of Integrals formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.