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    Mass and centroid of a Plane Lamina

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    Find the mass and centroid of a plane lamina with the given shape and density delta,
    the region bounded by y = x2 and x = y2 delta(x,y) = x2 + y2.

    © BrainMass Inc. brainmass.com May 24, 2023, 1:02 pm ad1c9bdddf


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    As you can see, the specified region is actually in the first quadrant. To find where the curves collide, it is enough to solve the equation:
    x^2=sqrt(x) which gives x=0 and x=1.
    Then we have:

    M= ...

    Solution Summary

    The mass and centroid of a plane lamina are determined through the use of double integrals.
    The solution is detailed and well presented.