Use triple integration in Cartesian coordinates to find the center of mass for the solid in the first octant bounded by the (XY, YZ, ZX) planes, and the surface z =4-x2-y, as shown in the figure? Use 8(x,y) = 15 Z-4-x-y

Find the centroid of the solid of revolution bounded by the curves x2y = 4, x 1, :4 and y = 0, rotated about the x-axis. 207 V = 3 cubic units; Centroid: (,0,0) None of the choices. Please refer to my solution. V = 217 cubic units; Centroid: (0, ",0) V = 21 cubic units; Centroid: (-",0,0) V = 217 cubic units; Centroid: (,0,0) 4

Find the surface area of the part of the surface z = x2 + 3y that lies above the triangular region T in the xy-plane with the vertices (0, 0), (1, 0), and (1, 11). Give your answer in 2 decimal places. You have to use the following formula: A (S) = 1+ + ду dA

Find the area of the part of the surface z = x2 + 2y that lies above the triangle with vertices (0,0), (1,0), and (0, 2).