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Math Help - Volumes of Revolution around the x-axis

  1. #1
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    Volumes of Revolution around the x-axis

    The question is:
    Find the volume generated when the finite region bounded by the given curves is rotated fully about the x-axis.

    y^4=16x, x=1, x=4, y=0

    If y^4=16x then y=2x - This is my curve.
    Are the x values the limits?

    Using the formula I can't get the correct answer. Can anyone help me out?

    Pi * Integral(limits 4-1) of 2x
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  2. #2
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    Quote Originally Posted by haku View Post
    The question is:
    Find the volume generated when the finite region bounded by the given curves is rotated fully about the x-axis.

    y^4=16x, x=1, x=4, y=0

    ...
    From

    y^4 = 16x you get | y | = 2 \sqrt[4]{x}

    The volume is calculated by:

    V = \pi \int \left(f(x)\right)^2 dx That means here:

    V=\int_1^4\left(2 \cdot x^{\frac14} \right)^2 dx

    V = \pi \left[4 \cdot \frac23 \cdot x^{\frac32} \right]_1^4

    I'll leave the rest for you.
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  3. #3
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    Washers:

    4{\pi}\int_{1}^{4}\sqrt{x}dx

    shells:

    4{\pi}\int_{2}^{2\sqrt{2}}\frac{y^{5}}{16}dy
    Last edited by galactus; February 24th 2008 at 12:25 PM. Reason: forgot to multiply by 2
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  4. #4
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    Okay so, [4.(2/3)x^(3/2)] Integrals 1 to 4

    [64/3] - [8/3] = (56/3)*Pi

    Is this correct?
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  5. #5
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    Yes, that's correct.
    Last edited by galactus; November 24th 2008 at 06:38 AM.
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