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Calculate Centroid of a Plane Region

I need to see how to find the centroid coordinates by using integrals and moments. I have attached a word document with the formulas we are supposed to use to find the centroid.

Now here is the problem:

Given: y = 9 - x^2, y = 2

Find the coordinates of the centroid of the above plane region.

Please refer to the attached file as well for extra information.


Solution Preview

f(x) = 9-x^2 = y; g(x) = 2 = y

1. Find the points of intersections of these two curves.

9-x^2 = 2 -> x^2 = 7 -> x = +/- sqrt(7); y = 2
Since the f(x)-g(x)area is below the parabola f(x), but above the line, y =2 is the ...

Solution Summary

This solution provides a detailed, step-wise solution of about 190 words which illustrates how to solve for the coordinates of a centroid of a plane region using integrals and moments. All calculations are included.