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Volume of solid rotated around y=1

  1. Mar 18, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the solid formed by revolving the region bounded by f(x) = 2-x^2 and g(x) = 1 about the line y = 1.



    2. Relevant equations
    V = ∏∫(1-f(x))^2dx - ∏∫(1-g(x))^2dx


    3. The attempt at a solution
    I keep ending up with ∏∫(1-(2-x^2))^2dx - ∏∫(1-1)^2dx, on the interval from x = 0, x = 1. This gives me ∏∫[(-1+x^2)^2 - 0]dx
    = ∏[x - (2/3)x^3 + (1/5)x^5].

    This keeps giving me 8∏/15.
    This is on a test review sheet, with the answer being 16∏/15. So I can get that answer by multiplying mine by 2, but why would I do that? I must be doing something wrong somewhere else. Any help would be greatly appreciated! Thanks.
     
  2. jcsd
  3. Mar 18, 2014 #2
    Hi jaguar ride! Welcome to PF!

    Sketch a plot of the given region. ;)

    You will notice that the integration limits are incorrect.
     
  4. Mar 18, 2014 #3
    Ah yes. Should have mentioned that a sketch is the first thing I do when solving these problems.
    That being said, I feel extra stupid for staring at this thing for so long and not realizing the limits could be negative.

    Got the answer. Makes sense that I could multiply it by 2 now...

    Thanks for your help and the warm welcome, I'll be back for physics help soon enough....
     
  5. Mar 18, 2014 #4
    Glad to help! :smile:
     
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