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Math Help - Integrals - Volume

  1. #1
    Member Awsom Guy's Avatar
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    Integrals - Volume

    Question:
    The region in the first quadrant bounded by the graphs f(x)=(1/8)(x)^3 and g(x)=2x is rotated about the y-axis. Find the volume of the solid formed.

    I know the integral basics.
    I think I have to place the y points and I think I am meant to convert the y= into x= so I have a x equation.

    This is what I got after integrating etc.

    ((6144/50)*(pi))-((512/12)*pi)).
    This I guess is not right.
    Thanks for any help.
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  2. #2
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    skeeter's Avatar
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    Quote Originally Posted by Awsom Guy View Post
    Question:
    The region in the first quadrant bounded by the graphs f(x)=(1/8)(x)^3 and g(x)=2x is rotated about the y-axis. Find the volume of the solid formed.
    using washers ...

    V = \pi \int_0^8 (2\sqrt[3]{y})^2 - \left(\frac{y}{2}\right)^2 \, dy<br />


    using cylindrical shells ...

    V = 2\pi \int_0^4 x \left(2x - \frac{x^3}{8}\right) \, dx
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  3. #3
    Member Awsom Guy's Avatar
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    Then I guess I do the normal Solving the function by subbing in the x values. thanks.
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