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Volume by rotating a curve

  1. Dec 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Hey i have a problem here with volume by cylindrical shells. i wanted to find the given volume of the solid obtained by rotating the region bounded by the curves x=1+(y-2)^2 and x=2 about the x axis.

    2. Relevant equations
    we tried to integrating 2 phi f(y) dy with upper limit 3 and lower limit 1.

    3. The attempt at a solution
    we got the answer 33.5 but i dont think it is the correct one.
    immediate help will be appreciable.
  2. jcsd
  3. Dec 9, 2009 #2


    Staff: Mentor

    You are using cylindrical shells, but your formula is incorrect. A typical shell in this problem has a volume of 2pi*y*(x2 - x1)*dy

    x2 is the x-value on the line x = 2, and x1 is the x-value on the parabola. You have graphed the region being revolved, right?
  4. Dec 10, 2009 #3
    can u tell me if my upper and lower limits are right because still i am not getting the right answer..i think!
  5. Dec 10, 2009 #4


    User Avatar
    Science Advisor

    Yes, the two curves intersect at (2, 1) and (2, 3) so y ranges between 1 and 3.
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