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Math Help - volume

  1. #1
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    volume

    Find the volume formed by rotating the region enclosed by:
    x=4y , y^3 = x, with y ≥ 0 about the y-axis.

    thanks for any help
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  2. #2
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    Graphing this, we can see it is symmetrical about the y-axis.

    Solve each for y in terms of x:

    y=\frac{x}{4}, \;\ y=x^{\frac{1}{3}}

    Set each equal and solve for x to find the limits of integration.

    Doing this, we see we get x=-8,0,8

    Using shells:

    2{\pi}\int_{0}^{8}x(\frac{x}{4}-x^{\frac{1}{3}})dx

    Integrating over -8 to 0 will yield the same result.

    Using washers, we can get the same thing.

    {\pi}\int_{0}^{2}\left[(4y)^{2}-(y^{3})^{2}\right]dy
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  3. #3
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    what do you get for a final answer for volume after integrating it? my answer is off i guess
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  4. #4
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    \frac{512\pi}{21}
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  5. #5
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    thanks a lot for the help!
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