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Volume using shell method

  1. Feb 1, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the solid generated by revolving the region bounded by y=4x-x^2 and y=x about the y-axis and about the line x=3.

    2. Relevant equations
    1. y=4x-x^2 and y=x
    2. y=4x-x^2 and x=3

    3. The attempt at a solution
    1. 2∏∫ (0 to 3) (x)(4x-x^2 -x) dx
    2. 2∏∫ (0 to 3) (3-x)(4x-x^2 -x) dx
  2. jcsd
  3. Feb 1, 2013 #2


    User Avatar
    Science Advisor

    Obviously you need to go ahead and actually subtract that last "x" in each formula: [itex]2\pi\int_0^3 x(3x- x^2)dx= 2\pi\int_0^3 3x^2- x^3 dx[/itex] and [itex]2\pi\int_0^3 (3- x)(3x- x^2)dx= 2\pi\int_0^3 9x- 6x^3+ x^3 dx[/itex] but, yes, those are set up correctly.
  4. Feb 1, 2013 #3


    Staff: Mentor

    What's your question?
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