Hello. I had a question about a few calculus examples. Thanks for your help! .

1)

For me lamina that occupies The region D bugunded by the curves 9'3 = y2 + 2 and'i = 2y 1, and has a density function: p(a:,y) = y+ 3. nd: a} the mass of the lamina; b] the moments of the lamina about xaxis and y-axis; c] the coordinates of the center of mass of the lamina. A cable, 8 m long, weighs 1 kg/m and hangs vertically from the top of the building. The cable is used to lift a full bucket that weighs 50 kg. Find the work done to pull the cable with the bucket to the top of the building. Assume g = 9. 8 m/ $2 . Your answer should include the following: a) Form the definite integral to evaluate the work done (7 marks). b) Work done obtained from the definite integral ( 3 marks). 8 m 50kg- bucket