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Finding a Centroid of a Region

Find the coordinates of the centroid of the region bounded by the curves y=3-x and y=-x^2+2x+3.

*I first found m or area, by rho(Integral 0 to 3)[(-x^(2) +2x +3) - (3-x)]dx and the result was 9rho/2.

Second, I found Mx, by rho (Integral 0 to 3) [(-x^2 +2x +3)+(3-x)/2][(-x^2 +2x +3)-(3-x)]dx and the result was 54rho/5, therefore y coordinate is 12/5.

Third, I found My, by rho (Integral 0 to 3) x[(-x^2 +2x +3)-(3-x)]dx and the result was 27rho/4, therefore x coordinate is 3/2.

Do these answers work out correctly?

Solution Preview

I am sure you know the basic steps of computing the centroid, but i am just going to go over them for completeness and in the process check your answers:

Step 1
Determine the function which is on TOP and which is on BOTTOM. To do that ...

Solution Summary

The centroid of a region is found using integrals.