Calculate Volume of Cylindrical Shells

[nobli1jl]

Use cylindrical shells to calculate the volume of the solid obtained by rotating the region bounded by y=x and y=x^2-2x about the line y=3
I know how do set the problem up and how to do it, I just don't know how to write "y=x^2-2x" in terms of "x". This is how I think the problem should be set up, with the changes made to the equation so everything in the equation will be "y's" or "dy's".

integrate from -1 to 0 : 2pi y (x^2-2x) dy + integrate from 0 to 3: 2pi y {y-(x^2-2x)} dy

 

[berkeman]

Welcome to PF, nobli. We are happy to be of help, but you must show us your work to start things off. Have you made a sketch of the volume? What coordinate system would probably be the easiest to use for this integration? What is the form of the dV vector in that coordinate system?


EDIT -- fixed a typo