## Math Problem Statement

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Centroid calculation

Parabolic region

Integration

### Formulas

Centroid formulas: \bar{x} = \frac{1}{A} \int_A x \, dA and \bar{y} = \frac{1}{A} \int_A y \, dA

Area element: dA = x(y) \, dy where x(y) = a \left[ 1 - \left( \frac{y}{b} \right)^2 \right]

### Theorems

Centroid calculation using integration

### Suitable Grade Level

Undergraduate (Engineering or Mathematics)

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