Explore BrainMass

Explore BrainMass

    Finding a Centroid of a Region

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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?

    © BrainMass Inc. brainmass.com March 6, 2023, 1:16 pm ad1c9bdddf

    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.