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MAT 273 Lab 3 - Centers of Mass - FA19 Name: Set up and show the integrals for each region or solid below and then calculate the center of mass. You may use technology. Round answers to 2 decimal places. Attach extra sheets as needed. 1. (18 points) Determine the center of mass of the region in the first quadrant bounded by y = 8 x2 if the density function is proportional to the height above the x-axis. 2. (18 points) Determine the center of mass of the triangular region with vertices (0,0), (5,0) and (0,12) if the density function is proportional to the distance from the y-axis and length is measured in inches. 3. (18 points) Determine the center of mass of the region inside r = 6 + 3 sin 6 if the density function is proportional to the distance from the pole. 4. (23 points) Find the center of mass of the solid bounded by 23: +3! + z = 2,22: = 32,315 = 0,2 = Owith densityfunction 6(x,y,z) = k . 8 i3 and length measued 1n meters. 111 5. (23 points) Find the center of mass of the solid between y = x2 +22 and y = 9. with density function 60:, y, z) = 12 y jg and length measured in feet