Please see the attached file for the fully formatted problem.
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.
Please see the attached file for the full solution.
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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:
The mass and centroid of a plane lamina are determined through the use of double integrals.
The solution is detailed and well presented.