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Math Help - solids of revolution

  1. #1
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    solids of revolution

    find the solid of revolution of the function lnx when it's rotated about the x-axis from 1 to e.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by nertil1 View Post
    find the solid of revolution of the function lnx when it's rotated about the x-axis from 1 to e.
    By the disk method, the required volume is given by:

    V = \pi \int_{1}^{e}( \ln x )^2 dx
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Jhevon View Post
    By the disk method, the required volume is given by:

    V = \pi \int_{1}^{e}( \ln x )^2 dx
    Now I'm curious. Just how do you go about integrating that?

    -Dan
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  4. #4
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    I tried this, and I still can't get it.

    What I did is  <br />
 2 \pi  \int_{1}^{e}( \ln x)^2 dx<br />
    and I get 2\pi, which I think is the right answer

    but I can't seem to do it with the method suggested.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by topsquark View Post
    Now I'm curious. Just how do you go about integrating that?

    -Dan
    by parts
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by nertil1 View Post
    I tried this, and I still can't get it.

    What I did is  <br />
 2 \pi  \int_{1}^{e}( \ln x)^2 dx<br />
    and I get 2\pi, which I think is the right answer

    but I can't seem to do it with the method suggested.
    here you are trying to use the shell method. in this case you need to change the function from a function of x to a function of y, and change the limits as well. by the way, the lnx should not be squared when using this method, and you have to multiply by the radius instead. personally, i think this is more work than its worth. use the disk method
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  7. #7
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    Re;

    Re:
    Attached Thumbnails Attached Thumbnails solids of revolution-32.gif  
    Last edited by qbkr21; June 9th 2007 at 01:30 PM.
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  8. #8
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by qbkr21 View Post
    Re:
    thanks for that qbkr21, but you forgot to multiply by \pi
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  9. #9
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    Re:

    I feel that this is awkward given that I have neven multiplied a pi times and e before...

    -qbkr21
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  10. #10
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by qbkr21 View Post
    I feel that this is awkward given that I have neven multiplied a pi times and e before...

    -qbkr21
    not to be a pain, but i think you also evaluated incorrectly. i think it should be  \pi (e - 2) .
    Last edited by Jhevon; June 9th 2007 at 08:04 AM. Reason: corrected a slight error in calculation
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  11. #11
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Jhevon View Post
    not to be a pain, but i think you also evaluated incorrectly. i think it should be  \pi (e - 2) .
    That agrees with the answer my calculator gave, anyway.

    -Dan
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  12. #12
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    Re:

    I agree you both. I made a mistake.

    Andrew
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