Example 2: Locate the centroid ( and ) of the shaded area with respect to the reference axes.
Solution: To solve for the centroid location, we must first choose an appropriate differential area. In this example, we choose a horizontal rectangle of width xand height dy.Differential area: dA = x dy
The x coordinate of the centroid is found as
To find the y coordinate of the centroid, we use the same differential element and write
Therefore, the centroid of the shaded area is at
Alternate Solution: Let's consider the solution with a different choice of differential element.Differential area: dA = dx dy
|Because of the choice of differential area, the integral over the area changes into a double integral over x and y. In this case, the selection of limits must consider the boundaries in x and y directions.|
The solution for the y coordinate of centroid can be obtained in a similar fashion.