Question

First, show all work for determining the mass of the planar lamina region in the first quadrant bounded by the circle ? 2 + ? 2 = 4 and the lines ? = 0 and ? = ? √3 with a density of ?(?, ?) = ? 2 . (Hint: You may want to use a double angle formula if using polar coordinates) Second, set up the double integrals for finding the moments My and Mx. Finally, use Wolfram Alpha to determine the center of mass of the planar lamina rounded to the hundredths place.

Answer 1

The region will be represented as:

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we need to find out the mass of shaded region

Mass,   

The region can be devided into two parts, and

For first region y varies from 0 to x and for second region y varies from 0 to

  

  

For the second function let,,