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Math Help - Volume around x axis

  1. #1
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    Volume around x axis

    x+y=1
    x=5-(y-2)^2

    Rotate around the x-axis, using the cylindrical shell method

    This is what ive came up with but its wrong


    2\pi\int_0^5 ((5-(y-2)^2+(1-y))(1-y) = \frac{145\pi}{6}

    Any help appreciated, thanks
    Last edited by silencecloak; February 8th 2009 at 12:01 PM. Reason: Fixed some typos
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  2. #2
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    Hello, silencecloak!

    x+y\:=\:1
    x\:=\:5-(y-2)^2

    Rotate around the x-axis, using the cylindrical shell method.
    Your limits are correct . . .

    The line has intercepts (1,0) and (0,1).
    The parabola opens to the left with vertex at (5,2).
    They intersect at (5,0) and (0,5).

    The formula is: . V \;=\;2\pi\int^b_a \text{(radius})\text{(height)}\,dy

    The radius is y.
    The height is: . \bigg[5-(y-2)^2\bigg] - \bigg[1 - y\bigg] \:=\:5y - y^2

    Then: . V \;=\;2\pi\int^5_0y(5y-y^2)\,dy

    Got it?

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  3. #3
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    Got it.

    Thanks
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