# Find the centroid of a lamina using Definite integrals when density of the region is a variable

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

A lamina is described with the help of three curves, given that density of the lamina at a point P is proportional to the square of its distance from x-axis and density at one of the points in the region of the lamina is also given. We need to find the centroid of the region.

For full text of the problem, please find the attachment.

Â© BrainMass Inc. brainmass.com March 6, 2023, 2:13 pm ad1c9bdddfhttps://brainmass.com/math/integrals/find-the-centroid-of-a-lamina-using-definite-integrals-when-density-of-the-region-is-a-variable-76761

#### Solution Preview

First the density function is estabilished, using the two given conditions. ...

#### Solution Summary

The centroid of a lamina using definite integrals is found when density of the region is a variable. The solution is detailed and well presented.

$2.49