Find the center of mass for the region bounded by y = x² and y = x + 2 with density p(x,y) = x.
To determine the bounded region, graph the given equations. (Please see attached figure.)
On the bounded region, draw a dot to represent its center of mass. To get its coordinates, we have to solve for its mass. Also, let's consider the bounded region as a thin plate.
The formula to compute its mass is:
`M = rho int_a^b f(x) - g(x)dx`
where ` rho ` represents the density, f(x) is the upper curve and g(x) is the lower curve.
The upper graph of the bounded region is y = x +2 and the lower curve is y=x^2. And bounded region starts at x=-1 and ends at x=2.
So, the mass of the plate is:
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