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Center of Mass $(2-$D sheets$)$

In each of these problems assume that the area described represents a sheet of constant density, so you are essentially finding the "center of the area".

Find the location of the center of mass $(\stackrel{}{x}\frac{,}{b}ar(y))$ of the sheet defined by the area underneath the line $f(x)=x+2,$ going from $x=0$ to $x=2.$

A sheet is defined as the area below the curve $f(x)=\frac{x^2}{2}$ going from $x=0$ to $x=2.$ Find the location of the center of mass $(\stackrel{}{x}\frac{,}{b}ar(y)).$

A sheet going from $x=1$ to $x=8$ is given as the regon under the curve $f(x)=10x^{-\frac{1}{3}}.$ Find the location of the center of mass $(\stackrel{}{x}\frac{,}{b}ar(y)).$

Find the center of mass $(\stackrel{}{x}\frac{,}{b}ar(y))$ of the sheet defined as the region between $f(x)=3x$ and $g(x)=x^2+3$ going from $x=0$ to $x=2($be careful about which is bigger!$).$

Find the coordinates for the center of mass $(\stackrel{}{x}\frac{,}{b}ar(y))$ of a uniform$-$density plane formed by the area between $f(x)=2x-6$ and $g(x)=x^{\frac{1}{2}}($starting at $x=0,$ and ending when these curves meet at $x=4).$