Represent the mass and moments of the region R, bounded by the function f(x) = x2+1\displaystyle {x}^{{2}}+{1} and the x-axis and the lines x=1 and x=5. Assume the mass density per unit of area is δ(x)=2\displaystyle \delta{\left({x}\right)}={2}.

Mass = M = ∫15\displaystyle {\int_{{\text{1}}}^{{\text{5}}}} dx   

Moment about y-axis = My = ∫15\displaystyle {\int_{{\text{1}}}^{{\text{5}}}} dx    

Moment about x-axis = Mx = ∫15\displaystyle {\int_{{\text{1}}}^{{\text{5}}}} dx     

Then calculate the center of mass for R (round to 2 decimal places):

 x‾\displaystyle \overline{{x}}  =

 y‾\displaystyle \overline{{y}} =

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