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Homework Help: Shell Method

  1. Dec 6, 2009 #1
    1. The problem statement, all variables and given/known data

    Have to find the volume using the shell method using the given curves

    x=3y-y^2 and the y-axis about the x-axis

    2. Relevant equations
    I know to use the equation V=2pi Integral y f(y) dy but no idea where to get the high and low limits for the integral

    3. The attempt at a solution
    Last edited: Dec 6, 2009
  2. jcsd
  3. Dec 6, 2009 #2


    Staff: Mentor

    Have you graphed the equation x = 3y - y^2? Its graph is a paraboloa that opens to the left. You can find the vertex of the parabola by completing the square in the y terms.

    Your typical volume element is [itex]\Delta V = 2\pi*y*x*\Delta y[/itex]. Since you will be integrating with respect to y, you need to replace x in this formula with 3y - y^2. From the graph you can also get the limits of integration.
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