# Mass and centroid of a Plane Lamina

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.

https://brainmass.com/math/calculus-and-analysis/mass-centroid-plane-lamina-9792

#### Solution Preview

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:

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.

$2.19