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Math Help - Find volume of a solid bound by 2 functions

  1. #1
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    Find volume of a solid bound by 2 functions

    Fins the volume if the solidobtained by rotating the region bounded by y=x^(1/3) and y=x/4
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  2. #2
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    Rotating it about what?. y-axis?. x-axis?. Some other axis?.

    Rotated about x-axis using washers:

    Find the limits of integration by setting them equal and solving for x. We get x=0 and 8.

    {\pi}\int_{0}^{8}(\frac{x^{2}}{16}-x^{\frac{2}{3}})dx

    Using shells rotated about x-axis:

    2{\pi}\int_{0}^{2}y(y^{3}-4y)dy
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  3. #3
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    that was exactly what the book said. I was a bit confused about it too. I think it means rotated about the xaxis
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  4. #4
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    Here is a happy little animated diagram showing the region rotated about the x-axis. Enjoy.

    And yes, that is what I gave you. Both methods rotating about the x-axis. Shells and washers.

    When we use shells, the cross sections are parallel to the axis about which we are revolving. Since they are parallel to the x-axis, we can picture them being stacked up the y-axis. That is why we integate w.r.t y in that case. We solve the equations for x in terms of y and change the limits to the y limits, which are 0 to 2.
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