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Math Help - Find the volume of the solid

  1. #1
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    Find the volume of the solid

    Find the volume of the solid that is generated by rotating the region formed by the graphs of y = x2, y = 2, and x = 0 about the y-axis.
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  2. #2
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    You can use shells or washers.


    Shells:
    2{\pi}\int_{0}^{\sqrt{2}}x(2-x^{2})dx


    Washers:
    {\pi}\int_{0}^{2}ydy
    Last edited by galactus; November 24th 2008 at 05:39 AM.
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  3. #3
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    sorry to be so ignorant at this, but using shells could you show me the rest of the answer?
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  4. #4
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    2{\pi}\int_{0}^{\sqrt{2}}x(2-x^{2})dx

    2 \pi \int_{0}^{\sqrt{2}} 2x-x^3dx

    Call the integral F(x)=x^2-\frac{x^3}{3}

    Thus the volume is 2\pi \left( F(\sqrt{2})-F(0) \right)

    Make sense?
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  5. #5
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    so if I did it right then, V = 6.64257 ?
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