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Calculus 2 Find the volume problem

  1. Mar 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the volume: y=x, y=0, x=2, x=4; about x=1

    2. Relevant equations

    Washer method V= ∏∫ (R)^(2)-(r)^(2) dy

    3. The attempt at a solution
    0 to 4 is my a to b**

    ∏∫(from 0 to 4) of (1-4)^(2)-(1-y)^(2) dy

    ∏∫(from 0 to 4) of 9-(1-2y+y^(2)) dy

    ∏∫(from 0 to 4) of 8 + 2y - y^(2) dy

    ∏[8y+y^(2)-y^(3)/3](from 0 to 4)

    ∏[32+16-64/3]=80∏/3


    That is my answer but I want to make sure that I got it correct. Thanks in advance!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 24, 2012 #2
    Hey people. So I reworked it and i got 76pi/3. Is this correct?
     
  4. Mar 25, 2012 #3
    I got 24∏. With rotations about the x axis it is usually easier to use cylindrical shells. It's much harder with washers, I don't even want to think about what you'd do for that. With cylindrical shells the integral would be from 0 to 4 of 2∏∫(x-1)x dx.
     
  5. Mar 25, 2012 #4
    Hey I ended up getting it. Thanks for taking the time to work it out. :smile:
     
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