Center of Mass Formulas: b r =i!x[f(x)g(x)lar b 7=il[[f(x)lz[g(x)lz]dr Consider the region bounded by the following curves to answer the following, providing exact values (not decimal approximations). f(1') = 31, 51(1) = 3.12 (a) Find the area, A, of the region. Provide a sketch of the region and show all work, including integration. A: (b) Find the center of mass (centroid), ()7, )7) , of the region (see formulas above). Plot this point on your sketched region from part (a). Show your work in setting up the integral, then integrate by hand or using Desmos (recommended). (Note: Do not use brackets if integrating in Desmos; use parentheses instead.) (W) =( , ) (c) Find the volume, V, of the solid obtained by revolving the region about the horizontal line y = -2. Provide a sketch of the solid and an arbitrary cross-section or cylindrical shell (depending on the method used). Show your work in setting up the integral, then integrate by hand or using Desmos (recommended). V= (d) Find the volume, V, of the solid obtained by revolving the region about the vertical line x = 1. Provide a sketch of the solid and an arbitrary cross-section or cylindrical shell (depending on the method used). Show your work in setting up the integral, then integrate by hand or using Desmos (recommended). v=