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Volume problem

  1. Mar 18, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by
    y = x^2
    y = 2x

    2. Relevant equations



    3. The attempt at a solution

    Okay, so I first solved both equations for y, which gave me x=radical(y) and x=y/2. Then I graphed both of them, found that the radical one was above the y/2, so I made the equation pi*(radical(y)^2 - (y/2)^2. I then made that equation a definite integral with lower limit 0 and upper limit 2.

    Of course, it turned out wrong (I'd use Latex to make it look nice, but it's not coming out very well right now and I don't have the patience). Suffice it to say, I did something wrong somewhere.
     
    Last edited: Mar 18, 2007
  2. jcsd
  3. Mar 18, 2007 #2

    Hootenanny

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    About which line are you rotating the region about, the x axis?
     
  4. Mar 18, 2007 #3
    Yes yes, the x axis. Sorry.
     
  5. Mar 18, 2007 #4

    Hootenanny

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    Then there is no need to solve for x. The volume of revolution about the a axis of a region bounded by two functions, f(x) and g(x) and the lines x=a and x=b is given by;

    [tex]V=\pi\int_a^b{\left|\left[f(x)\right]^2-\left[g(x)\right]^2\right|}dx[/tex]

    It my also be a good idea to sketch the two curves to get a visual idea of what your are actually doing.
     
    Last edited: Mar 18, 2007
  6. Mar 18, 2007 #5
    Ah okay, now I'm getting the right answer. Thanks.
     
  7. Mar 18, 2007 #6

    Hootenanny

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    No worries :biggrin:
     
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