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Math Help - intergrating

  1. #1
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    intergrating

    a) The graph of (Y= 2X^2) is rotated about the
    x-axis between (X=0) and (X=2). Express
    the volume of revolution 2 as a definite integral

    could someone talk me through this please?
    Last edited by bobchiba; May 7th 2007 at 09:31 AM.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by bobchiba View Post
    a) The graph of (Y= 2X^2) is rotated about the
    x-axis between (X=0) and (X=2). Express
    the volume of revolution 2 as a definite integral

    could someone talk me through this please?
    See the diagram below.

    We proceed by the disk method:

    V = int{A(x)}dx ................where A(x) represents the cross-sectional area of the circle obtained when rotating
    ...= int{pi*r^2}dx
    ...= int{pi*(2x^2)^2}dx
    ...= 4pi*int{x^4}dx from 0 up to 2

    and we leave it there since they just asked us to express it, not evaluate it. knowing the disk method you could just jump to the last line, all the other lines were just there to kind of explain what i was doing.
    Attached Thumbnails Attached Thumbnails intergrating-vol.gif  
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