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Math Help - Volume Using Shells

  1. #1
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    Volume Using Shells

    I can do volume fine about x and y=0, but I get messed up when it's about somewhere other than those.

    x+y=3, x=4(y-1)^2...Find the area rotating about the x axis.

    Can someone point me in the right direction?
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  2. #2
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    Quote Originally Posted by sfgiants13 View Post
    I can do volume fine about x and y=0, but I get messed up when it's about somewhere other than those.

    x+y=3, x=4(y-1)^2...Find the area rotating about the x axis.

    Can someone point me in the right direction?
    I'm guessing you really mean the volume ...

    3-y = 4(y-1)^2

    3-y = 4y^2 - 8y + 4

    0 = 4y^2 - 7y + 1

    y = \frac{7 \pm \sqrt{33}}{8}

    let c = \frac{7 - \sqrt{33}}{8}

    d = \frac{7 + \sqrt{33}}{8}

    V = 2\pi \int_c^d y[(3-y) - 4(y-1)^2] dy
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