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Math Help - Disk Method about the x axis

  1. #1
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    Disk Method about the x axis

    Does anyone know how to solve x(5-x)^(1/2) about the x axis using the disk method?
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  2. #2
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    Re: Disk Method about the x axis

    Quote Originally Posted by crzyberzu123 View Post
    Does anyone know how to solve x(5-x)^(1/2) about the x axis using the disk method?
    I assume the area formed between the graph of the function and the x-axis in quadrant I ... ?

    V = \pi \int_0^5 \left(x \sqrt{5-x} \right)^2 \, dx
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    Re: Disk Method about the x axis

    Would you set the equation equal to x so that you could make everything in terms of y?
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    Re: Disk Method about the x axis

    Quote Originally Posted by crzyberzu123 View Post
    Does anyone know how to solve x(5-x)^(1/2) about the x axis using the disk method?
    May I re-write the question as I understand it?:

    Determine the volume when the area, enclosed by the x-axis and the graph of y = x \cdot \sqrt{5-x}, rotates about the x-axis.

    Quote Originally Posted by crzyberzu123 View Post
    Would you set the equation equal to x so that you could make everything in terms of y?
    The volume is composed by cylindrical discs whose radius is y and whose height is dx. The volume of one of these discs is calculated by:

    V_{single\ disc} = \pi \cdot y^2 \cdot dx

    The complete volume of the solid is the sum of all those discs:

    V=\int (\pi \cdot y^2)dx

    Plug in the term of y and determine the borders of the area and you'll get the equation skeeter has posted.
    Last edited by earboth; April 11th 2012 at 11:00 AM.
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