We consider a thin plate of constant density 
 occupying the region of the plane bounded by a closed curve C.

a) Using Green's theorem, show that the center of mass of the plate of the plate can be calculated using the formulas :

where m is the mass of the plate.

b) Determine the center of mass of a thin plate occupying the region delimited by the curve C parameterized by :

knowing that the mass of the plate is m = 11π 

Curve C is shown below :

You can use software or the reduction formulas to evaluate integrals.

 
 
 
 
 

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