Applications of Integrals · Centroids & Averages
Centroid (y-coordinate)
The y-coordinate of the centroid of the region between f(x) and g(x).
- 2 variables
- 2 worked examples
- 14 in Applications of Integrals
Variables
| Symbol | Name | Unit |
|---|---|---|
| a | Left bound | - |
| b | Right bound | - |
Worked examples
- A = 8/3
- ȳ = (3/8)(1/2) ∫₀² (x²)² dx = (3/16) ∫₀² x⁴ dx = (3/16)(32/5) = 6/5
Answer: ȳ = 6/5
1 more worked examplePremium
Step-by-step solution locked.
See all 14 Applications of Integrals formulas on one printable sheet - the same statements and conditions as these pages, typeset and laid out for paper.
Common questions
What is the Centroid (y-coordinate)?
The y-coordinate of the centroid of the region between f(x) and g(x). It is one of the applications of integrals formulas in the CalcRef reference.
What do the symbols in the Centroid (y-coordinate) mean?
In the Centroid (y-coordinate), a is the left bound; b is the right bound.
How do you use the Centroid (y-coordinate)?
Worked example. Find ȳ for the region under y = x² on [0, 2]. A = 8/3. ȳ = (3/8)(1/2) ∫₀² (x²)² dx = (3/16) ∫₀² x⁴ dx = (3/16)(32/5) = 6/5. Answer: ȳ = 6/5.
Practice
Quiz yourself on Applications of Integrals
Centroid (y-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.