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

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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.

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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.

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

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