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Math Help - Area & Volume Using Integrals

  1. #1
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    Area & Volume Using Integrals

    I can't get the answer which I think I'm supposed to be getting. Could someone please go through this so I'll understand it.

    Sketch the area A defined by y = x(1-x) and the x-axis.
    a) compute the volume when the area is revolved by the line y = -2.
    b) compute volume when area is revolved about line x = -2


    I am 99.9% positive that the volumes should be the same when you solve using both the x and y lines, but I am getting different answers. Please help!!!
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  2. #2
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    Quote Originally Posted by TreeMoney View Post
    I can't get the answer which I think I'm supposed to be getting. Could someone please go through this so I'll understand it.

    Sketch the area A defined by y = x(1-x) and the x-axis.
    a) compute the volume when the area is revolved by the line y = -2.
    Shift the coordinate axes by 2 units upward then it is the same as about y-axis
    Thus,
    integral^1_0 pi [x(1-x)-2]^2dx
    Quote Originally Posted by MoneyTree
    b) compute volume when area is revolved about line x = -2
    Shift the coordinate axes by 2 units to the right, thus, x becomes x-2, which as the same as the area bout x-axis
    Thus,
    2pi*integral_2^3 x[(x-1)(-x)] dx
    Note the change in the limits on integration because I made a shift.
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