1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook