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Volume Shell Method

  1. Feb 1, 2013 #1
    1. The problem statement, all variables and given/known data
    use the shell method to find the volumes of the solids generated by revolving the region about the indicated axis.


    2. Relevant equations
    x=18(y^2 - y^3) about line y=8/5.


    3. The attempt at a solution
    2∏∫ (0 to 1) (8/5 - y) (18y^2 - 18y^3)
     
  2. jcsd
  3. Feb 1, 2013 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    This single equation does not define a bounded region. Was there some other line or curve given, such as the y-axis (x= 0)?


     
  4. Feb 1, 2013 #3
    according to the graph it appears bounded by y-axis. (x=0)
     
  5. Feb 1, 2013 #4

    Mark44

    Staff: Mentor

    Assuming that the region to be revolved is between one arch of the curve and the y-axis, your setup looks fine, except that you are missing the differential. It might not seem important now, but when you learn more techniques of integration, omitting the differential will be a big problem.



    What do you get for the value of your integral?
     
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