One of my friends ask me a question but I don't know how to deal with upside down issue... Here it is:
Consider the region in the plane bounded by the graph of y=x^3+36x^2+432x, 0<=x<=3 on the left, by x-axis along the bottom, by the line y=1647 along the top, and by the line x=7 along the right. Suppose the region is resolved around x=12, so as to produce a solid of revolution. Find the new work done in turning this solid upside down. Assume that the solid is 9400kg per cubic meter and units along coordinate axes are measured in meters. Express your answer in terms of joules. The integral for work may be expressed as....?