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Math Help - shell method

  1. #1
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    shell method

    Find the volume of the solid formed by revolving the region bounded by the graph of f(x)=4-x^2 and the x-axis about the line x=3 using the shell method.
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  2. #2
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    2\pi \int_{0}^{4} rhdy

    r = 3 - y

    h = \sqrt {4 - y}

    2\pi \int_{0}^{4} (3 - y)\sqrt {4 - y}dy

    u = 4 - y
    dy = -dy

    -\int (u + 1)\sqrt udu = -\int (u^{3/2}du + \sqrt udu)
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  3. #3
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    Quote Originally Posted by derfleurer View Post
    2\pi \int_{0}^{4} rhdy

    r = 3 - y

    h = \sqrt {4 - y}

    2\pi \int_{0}^{4} (3 - y)\sqrt {4 - y}dy

    u = 4 - y
    dy = -dy

    -\int (u + 1)\sqrt udu = -\int (u^{3/2}du + \sqrt udu)
    how can u replace 3 in 3-y?
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