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Math Help - Shell Method Help

  1. #1
    Junior Member xfriendsonfirex's Avatar
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    Shell Method Help

    Here's the problem. I just have difficulty figuring out the problems where you are revolving a shape around something other than the x or y-axis. Any help would be greatly appreciated.

    Here's the full problem:

    Use the shell method to find the volume of the solid generated by revolving the plane region about the given line.

    y=x^2, y=4x-x^2, about the line x=4
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  2. #2
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    Quote Originally Posted by xfriendsonfirex View Post
    Here's the problem. I just have difficulty figuring out the problems where you are revolving a shape around something other than the x or y-axis. Any help would be greatly appreciated.

    Here's the full problem:

    Use the shell method to find the volume of the solid generated by revolving the plane region about the given line.

    y=x^2, y=4x-x^2, about the line x=4
    V = 2\pi \int_a^b \textcolor{red}{r(x)} \cdot \textcolor{blue}{h(x)} \, dx

    V = 2\pi \int_0^2 \textcolor{red}{(4-x)}\textcolor{blue}{[(4x-x^2) - x^2]} \, dx
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by xfriendsonfirex View Post
    Here's the problem. I just have difficulty figuring out the problems where you are revolving a shape around something other than the x or y-axis. Any help would be greatly appreciated.

    Here's the full problem:

    Use the shell method to find the volume of the solid generated by revolving the plane region about the given line.

    y=x^2, y=4x-x^2, about the line x=4
    the nice thing with the shell method is that the only major change happens on the radius. recall that for dx-problems, the radius is right - left.

    the distance from the y-axis to the object is x. and your axis of rotation is given. just figure out which is on the right.

    here, if you draw a diagram, you will realize that the axis of rotation is on the right of the region you are revolving. the axis is 4, the region is at a distance x, so the radius is right - left = (axis of rot.) - (distance from y-axis) = 4 - x

    now do the Shell method with that radius.
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  4. #4
    Junior Member xfriendsonfirex's Avatar
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    Awesome, got it. Thanks!
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