Find the center of mass of the region in the first quadrant bounded by y=x^2-1 and x=2 in each scenario:
a)assuming constant density
b)assuming the density at a point in the region is given by ᵟ(y)=y
c)assuming the density at a point in the region is given by ᵟ(x)=x^2

Question

Find the center of mass of the region in the first quadrant bounded by y=x^2-1 and x=2 in each scenario:
a)assuming constant density
b)assuming the density at a point in the region is given by ᵟ(y)=y
c)assuming the density at a point in the region is given by ᵟ(x)=x^2

foolaroundmath · Answer

$$\large (x_{cm},y_{cm})= \left ( \frac{\int \int x\rho(x,y) dx dy}{\int \int \rho(x,y) dxdy},\frac{\int \int y\rho(x,y) dxdy}{\int \int \rho(x,y) dxdy}  \right ) $$