Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Centroid calculation
Area integration
Curve integration

Formulas

Area under a curve: A = ∫f(x) dx
Centroid (x-coordinate): \( \bar{x} = \frac{1}{A} \int x dA \)
Centroid (y-coordinate): \( \bar{y} = \frac{1}{A} \int y dA \)

Theorems

Centroid of composite areas
Integral of a curve (area under a curve)

Suitable Grade Level

Undergraduate level, Engineering or Physics courses