Center of Gravity, Centroid

Example: Find the y-coordinate of the centroid for the shaded area shown in the figure below.

Strategy:

1.	Use the principle of first moments. i.e. ycg A = ∫ y dA
2.	Show the element of area, dA and use it to calculate A the total area.
3.	Show the element of area, dA and use it to calculate y dA .
4.	Determine the limits of integration for ∫ y dA.
5.	Perform the integration and use it to solve for ycg. i.e. ycg = ∫ y dA / A

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