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Homework Help: Disc Method

  1. Apr 30, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the volume of a solid formed by revolving the region bounded by graphs of:
    y=x^3
    y=1
    and
    x=2


    2. Relevant equations
    [tex]\pi[/tex]0[tex]\int[/tex]2(x^3)dx


    3. The attempt at a solution

    x^7/7 with boundaries of [0,2]

    Am I on the right path?
     
  2. jcsd
  3. Apr 30, 2008 #2

    Dick

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    That's ok if you ignore the y=1 boundary, but I don't think you should. Draw a picture. I presume you are rotating around the x-axis?
     
  4. Apr 30, 2008 #3

    HallsofIvy

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    Revolved around what axis?


    If you are the x-axis and are using the disk method, you would be integrating [itex]\pi\int_0^1 y^2 dx+ \pi\int_1^2 1 dx[/itex]


     
  5. Apr 30, 2008 #4
    Yes, rotating around the x-axis.
     
  6. Apr 30, 2008 #5

    tiny-tim

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    Hi frumdogg! :smile:

    That doesn't look solid … do you mean y = 2 ? :confused:
     
  7. Apr 30, 2008 #6
    The problem says
    y=x^3
    y=1
    x=2

    When graphing it, it's a small area with x^3 on the left, y=1 on top, x=2 on right, and x axis on bottom, at least what I am coming up with.
     
  8. Apr 30, 2008 #7

    tiny-tim

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    hmm … they might as well have said:

    y=x^3
    x=1;

    the rest is just a cylinder. :confused:
     
  9. Apr 30, 2008 #8

    Dick

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    It's a region with y=0 at the bottom and y=x^3 at the top from x equal 0 to 1 and y=1 at the top and y=0 at the bottom from x equal 1 to 2. Halls already set it up for you. tiny-tim is saying the same thing.
     
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