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**preview**shows half of the first page. to view the full**1 pages of the document.**8.3 Challenging Integral Applications

Physics & Engineering Applications

Question #6 (Medium): Finding the Coordinate of the Centroid

Strategy

For a region bound by continuous functions, the location for the coordinate for the centroid is calculated

as:

and

. Thus,

Sample Question

Sketch the area bound by the function and visually estimate the location of the centroid. Then

determine the exact coordinate the centroid.

, , ,

Solution

From the graph, the bound region is right and down heavy. So it is and

and can be guess to be around and

The total mass is calculated as the whole area of the bound region. Here,

Now, moment of the system about the x-axis is:

. Likewise,

the moment of the system about the y-axis is:

Therefore, the location of the centroid is:

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